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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.(i) 525 (ii) 1750 (iii) 252 (iv) 1825(v) 6412 |
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Answer» (i) `23^2 > 525 > 22^2` to make it square , add `= 23^2 - 525` `= 529 - 525 = 4` new number =`525 +4 = 529` `sqrt529 = 23` (ii) `80^2 < 6412 < 81^2` add `81^2 - 6412` `= 6561 - 6412` `= 149` (iii) `15^2 < 252 < 16^2` add `= 16^2 - 252` `= 256 - 252= 4` answer |
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| 2. |
Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.(i) 402 (ii) 1989 (iii) 3250 (iv) 825(v) 4000 |
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Answer» (i)`402 = 20^2 +2` So, if we subtract `2` from `402`, we get a perfect square and square root of the perfect square will be `20`. (ii) `1989 = 44^2+53` So, if we subtract `53` from `1989 `, we get a perfect square and square root of the perfect square will be `44`. (iii) `3250 = 57^2+1` So, if we subtract `1` from `3250 `, we get a perfect square and square root of the perfect square will be `57`. (iv) `825 = 28^2+41` So, if we subtract `41` from `825 `, we get a perfect square and square root of the perfect square will be `28`. (v)`4000 = 63^2+31` So, if we subtract `31` from `4000 `, we get a perfect square and square root of the perfect square will be `63`. |
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| 3. |
Find the least number that must be subtracted from 5607 so as to get a perfect square. Also find the square root of the perfect square.find the greatest 4 digit number which is a perfect square . |
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Answer» If we try to calculate the square root of `5607`, then we get a remainder `131`. So, if we subtract `131` from `5607` then we get a perfect square. So, perfect square = `5607 - 131 = 5476` The square root of `5476 = 74` The greatest 4-digit number is `9999`. If we try to calculate its square root, then the remainder is `198` So, if we subtract `198` from `9999` then we get a perfect square. So, greatest 4-digit number having perfect square = `9999 - 198 = 9801` |
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| 4. |
2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row. |
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Answer» Let there be total x rows Then columns will also be x According to question x*x=2025 x=45 Total number of rows and columns =45 |
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| 5. |
Find the square roots of the following numbers by the Prime Factorisation Method.(i) 729 (ii) 400 (iii) 1764 (iv) 4096(v) 7744 (vi) 9604 (vii) 5929 (viii) 9216(ix) 529 (x) 8100 |
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Answer» (i) `729 = 3 xx 3 xx 3 xx3 xx 3 xx3` `sqrt 729 = 3 xx 3 xx 3 = 27` (iii) `1764= 2 xx 2 xx 3 xx 3 xx 7 xx 7` `sqrt 1764 = 2 xx 3 xx 7 = 42` (v) `7744 = 2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 11 xx 11 ` `sqrt 7744 = 2 xx 2 xx 2 xx 11 = 88` (vii) `5929 = 7 xx 7 xx 11 xx11` `sqrt 5929 = 7 xx 11 = 77` (ix) `529 = 23 xx 23` `sqrt 529 = 23` answer |
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| 6. |
Find the square roots of 100 and 169 by the method of repeated subtraction. |
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Answer» 1)100 100-1=99 99-3=96 96-5=91 91-7=84 84-9=75 75-11=64 64-13=51 51-15=36 36-17=19 19-19=0 There are total 10 numbers So, 10 is the square root of 100 2)169 169-1=168 168-3=165 165-5=160 160-7=153 153-9=144 144-11=133 133-13=120 120-15=105 105-17=88 88-19=69 69-21=48 48-23=25 25-25=0 There are total 13 numbers So, 13 is the square root of 169. |
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| 7. |
If a and b are whole number such that `a^(b)=512` where a `gt` b and 1 `lt` b `lt` 4 then `bsqrt(a)`=A. 2B. 3C. 4D. cannot be determined |
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Answer» Correct Answer - a (i) Express 512 as `a^(b)` (ii) Use the given conditions and evaluate the valuses of a nad b (iii) Write all possible exponential forms of 512 (iv)Get the required exponential form as per the given condions |
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| 8. |
Which of the following number becomes a perfect cube when we divide the number by 5?A. 25B. 125C. 325D. 3125 |
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Answer» Correct Answer - c Divide each option by 5 and check for the answer |
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| 9. |
A number is multipled by `2(1)/(3)` times itself and then 61 is substracted from the product obtained .If the final result is 9200 then the number isA. 36B. 63C. 67D. 37 |
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Answer» Correct Answer - b (i) Frame a simple equation by taking the number as x (ii) `x xx 2(1)/(3)x-61=9200` find x |
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| 10. |
The least number to be substracted from 220 so that it become a perfect cube isA. 4B. 10C. 16D. 20 |
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Answer» Correct Answer - a Apply successiv subtraction method |
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| 11. |
Is 2352 a perfect square? if no, find the smallest multiple of 2352 which is a perfect square. also find the square root of the new number? |
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Answer» LCM(2352)=2*2*2*2*3*7*7 No, 2352 is not a perfect square. If this number will be multiplied by 3 then this will be perfect square new number=2*2*3*7=84. |
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| 12. |
Find the divisor given that the dividend is 2200 remainder is 13 the divisor is one third of the quotientA. 25B. 27C. 24D. none of these |
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Answer» Correct Answer - b (i) Use divident =quotient `xx` diviso + remainder (ii) Consider the quotient as x (iii) Use division algorithm i.e dividend =(divisor `xx` quotient )+remainder |
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| 13. |
A certain number of men went to a hotel .Each man spent as mamy rupee as one fourth of the men.If the total bill paid was Rs 20449 then how many men visited the hotel?A. 286B. 284C. 281D. 283 |
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Answer» Correct Answer - a Form a simple equation and solve (i) Consider the number of men as x (ii) Total bill paid =(Numbr of men)`xx`(Amount spent by each men) |
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| 14. |
Find the square root of 12.25. |
| Answer» Square root of 12.25 = 3.5 | |
| 15. |
A man purchased a plot which is in the shape of a square .The area of the plot is 12 hectares 3201 `m^(2)` .Find the length of each side of the plot (in m)`A. 349B. 351C. 359D. 361 |
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Answer» Correct Answer - b 1 hectare = 10000 `m^(2)` (i) 1 hectare =10000 `m^(2)` (ii) As A=`S^(2)=sqrt(A)` |
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| 16. |
Area of square plot is 6561 `m^(2)` find the length of a diagonal of the square plot . The following are the steps involved in solving the above problem Arrange them in sequential order (A) Area of the square plot =`sqrt(2)xxx=81sqrt(2)m` (B) Length of the diagonal =`sqrt(2)xxx=81sqrt(2)m` (C )Let the side of the square plot be x cm (D) `therefore` side of the square plot x=`sqrt(6561) =81 m`A. DCBAB. BCADC. CADBD. ABDC |
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Answer» Correct Answer - c cadb is the sequential order of steps |
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| 17. |
Area of a square plot is `2304m^2.` Find the side of the square plot. |
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Answer» Let the side of plot be x According to Question x*x=2304 x=48. Side of plot is 48 m. |
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| 18. |
The length of a diagonal of a square plot is 24 cm find the area of the square plot. The following are the steps involed in solving the above problem .arrange them in sequential order (A) Area of the square plot =`1/2xx(24)^(2) =288cm^(2)` (B) Given that hte length of diagonal of a square plot (d)=24 cm (C ) Are of a square when diagonal is given is `1/2 d^(2)`A. CABB. BCAC. ABCD. BAC |
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Answer» Correct Answer - b BCA is the sequential order of steps |
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| 19. |
There are 2401 students in a school. P.T. teacher wants them to stand in rows and columns such that the number of rows is equal to the number of columns. Find the number of rows. |
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Answer» Let the total number of rows be x Then total number of columns be x According to Question x*x=2401 x=49 students Total number of rows are 49. |
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| 20. |
There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement. |
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Answer» As the number of rows is equal to the number of columns, we can take a square root of the total number of children. If we take the square root of `500`, we have a remainder `16`. It means `484` children can be arranged in `22` rows and `22` columns and rest `16` will be left out. |
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| 21. |
The following numbers are obviously not perfect squares. Give reason.(i) 1057 (ii) 23453 (iii) 7928 (iv) 222222(v) 64000 (vi) 89722 (vii) 222000 (viii) 505050 |
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Answer» A number can be a perfect square only when it has unit digit among `1,4,9,6,5`. In all the given numbers, the unit digit is not equal to any of digits `1,4,9,6,5`. So, all given numbers are not perfect squares. |
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| 22. |
If `sqrt (1+(49)/(576))=1+x/(24)`, then the value of x is |
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Answer» `1 + 49/576 = (1 + x/24)^2` `1+ 49/576 = 1 + x^2/576 + 2x/24` `49/24 = x^2/24 + 2x` `49/24 = (x^2 + 48x)/24` `x^2 + 48x - 49 = 0` `x^2 + 49x - x - 49= 0` `(x+49)(x-1) = 0` `x=-49, 1` `x=-49` cannot be possible so,`x=1` option A is correct |
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| 23. |
Express `13^2` as a sum of two consecutive natural number |
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Answer» `169=n+(n+1)` `2n+1=169` `2n=168` `n=84` 84,85. |
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| 24. |
What will be the unit digit of the squares of the following numbers?(i) 81 (ii) 272 (iii) 799 (iv) 3853(v) 1234 (vi) 26387 (vii) 52698 (viii) 99880(ix) 12796 (x) 55555 |
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Answer» Unit digit of a square of a number is equal to the unit digit of square of unit digit of that number. So, (i)`81` - Unit digit of square of `81` will be `1`. (ii)`272` - Unit digit of square of `272` will be `4`. (iii)`799` - Unit digit of square of `799` will be `1`. (iv)`3853` - Unit digit of square of `3853` will be `9`. (v)`1234` - Unit digit of square of `1234` will be `6`. (vi)`26387` - Unit digit of square of `26387` will be `9`. (vii)`52698` - Unit digit of square of `52698` will be `4`. (viii)`99880` - Unit digit of square of `99880` will be `0`. (ix)`12796` - Unit digit of square of `12796` will be `6`. (x)`55555` - Unit digit of square of `55555` will be `5`. |
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| 25. |
(i) Express 49 as the sum of 7 odd numbers.(ii) Express 121 as the sum of 11 odd numbers. |
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Answer» Any perfect square can be represented as the sum of first `n` odd numbers where `n` is the square root of the number. So,(i) `49 = 1+3+5+7+9+11+13` (ii)`121 = 1+3+5+7+9+11+13+15+17+19+21` |
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| 26. |
Observe the following pattern and supply the missing numbers. `11^2 = 121 101^2 = 10201 10101^2 = 102030201 1010101^2 = .........2 = 10203040504030201` |
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Answer» `11^2 = 121` `101^2 = 10201` `10101^2 = 10203020101` `1010101^2 = 102030403020101` `101010101^2 = 1020304050403020101` |
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| 27. |
In an Atlas, a map occupies `1/5th` of a page with dimensions `25 cm` and `30 cm` respectively. If the real area of the map is `194400 m^2`, the scale to which the map is drawn, isA. 1cm = 36xB. 1 cm = 26 mC. 1 cm = 33 mD. 1 cm = 23 m |
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Answer» Correct Answer - a (i)Area occupied by the map =The real area of the map (ii) Area of map =1/5 (Area of page) (iii) Area of map = 194400 `m^(2)` (iv) Use the concept area on map = Area on the ground. |
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| 28. |
`3sqrt(-a^(6)xxb^(3)xxc^(31))/(c^(9)xxa^(12))`A. `(-bc^(3))/(a^(2))`B. `(bc^(4))/(a^(2))`C. `(-ab^(4))/(c^(2))`D. `(-bc^(4))/(a^(2))` |
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Answer» Correct Answer - d use `(a^(m))/(a^(n))=a^(m-n)`and `a^(m)xxa^(n)=a^(m+n)` |
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| 29. |
The smallest number with which 120 should be multiplied so that the product is a perfect square isA. 120B. 60C. 30D. 15 |
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Answer» Correct Answer - c Write the prime factors from the number 120 |
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| 30. |
If `sqrt(x)+(58)/(sqrt(x))` =31 then which of the following can be the value of x?A. 529B. 931C. 729D. 841 |
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Answer» Correct Answer - d `sqrt(x)+(58)/(sqrt(x))=31` Since 31 is an integer `(588)/(sqrt(x))` must be an integer `therefore sqrt(x)` can be 29 or 2 `rarr` x =841 or 4 |
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| 31. |
The cube of the number p is 16 times the number Then find p where p `ne`A. 4B. 3C. 8D. 2 |
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Answer» Correct Answer - a `P^(3)=16p` |
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| 32. |
Which of the following is not a perfect square ?A. 12544B. 3136C. 23832D. 1296 |
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Answer» Correct Answer - c Perfect square never ends with 2,3,7 and 8 |
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| 33. |
The value of `sqrt(117^(2)-108^(2))`A. 55B. 45C. 35D. 65 |
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Answer» Correct Answer - b Use `a^(2)-b^(2)=(a+b)(a-b)` |
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| 34. |
The least 4 digit number which is a perfect square isA. 1024B. 1016C. 1036D. 1044 |
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Answer» Correct Answer - a Select the perfect square which is closed to 1000 |
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| 35. |
If the product of two equal numbrers is 1444 then the number areA. 48,48B. 38,38C. 32,32D. 42,42 |
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Answer» Correct Answer - b The required number is `sqrt(1444)` |
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| 36. |
What will be the units digit of the squares of the following numbers?A. 71B. 669C. 2533D. 30827 |
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Answer» Correct Answer - c (i) Squre the units digit of the given number (ii) The units digit of the above obtained number is the requaired result |
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| 37. |
The cube of a number ending in 3 ends in _____________A. 3B. 7C. 9D. cannot say |
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Answer» Correct Answer - b Recall the properties of cube |
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| 38. |
The square root of `36/5` when corrected to two decimal places isA. 2.68B. 2.69C. 2.67D. 2.66 |
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Answer» Correct Answer - a Evaluate square root by division method |
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| 39. |
If the units digits of a perfect square is 4 then the units digit of its square root can beA. only aB. only bC. Either a or bD. Neither a nor b |
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Answer» Correct Answer - c Recall the properites of square roots |
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| 40. |
The cube root of 110592 is ________A. 44B. 38C. 58D. 48 |
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Answer» Correct Answer - d write the prime factors for the number 110592 |
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| 41. |
The cube root of the number 10648 is ___________A. 42B. 38C. 28D. 22 |
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Answer» Correct Answer - d `10648=x^(3)` |
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| 42. |
In a four digit number 5a3b `agtb` and `a=b^(3)` .Then the differecne of the number and its cube root isA. 5850B. 5220C. 5256D. 5814 |
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Answer» Correct Answer - d (i) `a=b^(33)` possible when b =1 or 2 (ii) Consider 5a3b as a perfect cube and get the values of a and b using `=b^(3)` and `agtb` (iii) As a `agtb` and `a=b^(3)` a is the greatest possible single digit perfect cube (iv) Evaluate its cube root and subtract form the number |
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| 43. |
The square root of 102 up to three places of decimals isA. 10.098B. 10.099C. 10.097D. 10.096 |
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Answer» Correct Answer - b Use division method to find squar root |
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| 44. |
Find the square root of each of the following numbers by Division method.(i) 2304 (ii) 4489 (iii) 3481 (iv) 529(v) 3249 (vi) 1369 (vii) 5776 (viii) 7921(ix) 576 (x) 1024 (xi) 3136 (xii) 900 |
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Answer» `(i) 2304 =2^8 xx 3^2 `its square root`=48` `(ii) 4489=(67)^2` its square root`=67` `(iii) 3481=(59)^2` its square root`=59` `(iv) 529=(23)^2` its square root`=23` `(v) 3249=3^2xx19^2`its square root`=57` `(vi) 1369=(37)^2` its square root`=37` `(vii) 5776=2^4xx19^2`its square root`=76` `(viii) 7921=89^2`its square root`=89` `(ix) 576=2^6xx 3^2 `its square root`=24` `(x) 1024=2^10`its square root`=32` `(xi) 3136=2^6xx 7^2 `its square root`=56` `(xii) 900=`its square root is 30. |
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