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51.

If we add first n numbers, we get ______(a) \(\frac{n (n+1)}{2}\)(b) n-1(c) n^2(d) n^2-1The question was asked in my homework.I want to ask this question from Patterns in Squares in chapter Squares and Square Roots of Mathematics – Class 8

Answer»

Right option is (a) \(\frac{n (n+1)}{2}\)

Explanation: If we add FIRST n numbers we get \(\frac{n (n+1)}{2}\). For example, if we add 1 + 2 + 3 + 4 + 5, we get 15.

Here, we added first 5 numbers. Here, \(\frac{n (n+1)}{2} = \frac{5 (5+1)}{2} \)= 15.

Hence, \(\frac{n (n+1)}{2}\) would be the CORRECT answer and the other OPTIONS would be INCORRECT.
Discussion
52.

What would be the square of 1111?(a) 1234321(b) 12321(c) 121(d) 1I got this question in homework.I'm obligated to ask this question of Patterns in Squares in chapter Squares and Square Roots of Mathematics – Class 8

Answer» RIGHT option is (a) 1234321

To explain I would say: The squares of all the numbers with only 1 as its digit in all its places have a special pattern.

If we need to find the SQUARE of number 11, we can write 121. Similarly, square of number 111 is 12321. Therefore, we have the answer without calculating this HUGE number.
Discussion
53.

If we add first n odd numbers, we get ______(a) n(b) n-1(c) n^2(d) n^2-1This question was posed to me during an interview.My doubt stems from Patterns in Squares in division Squares and Square Roots of Mathematics – Class 8

Answer»

The CORRECT option is (c) n^2

Easy explanation: If we add FIRST n odd numbers we get n^2. For example

1+3+5=9=3^2, here we have added first three odd numbers and we get 3^2.

Hence, n^2 WOULD be the correct ANSWER and the other options would be INCORRECT.
Discussion
54.

________ is the general formula to find the number of non-square numbers in between two consecutive squares.(a) n^2+2n-1(b) n^2-1(c) 2n+1(d) n+1I have been asked this question during an interview for a job.The above asked question is from Patterns in Squares topic in section Squares and Square Roots of Mathematics – Class 8

Answer»

Correct ANSWER is (c) 2n+1

Easiest EXPLANATION: If we want to find the general formula for the number of non-square numbers in between two consecutive SQUARES, we assume to the natural numbers to be N & n+1

We square and subtract the SMALLER from the greater number,

(n+1)^2-n^2=(n^2+2n+1)-n^2=2n+1
Discussion
55.

If we combine two consecutive triangular numbers, we get?(a) Rational Number(b) Whole Number(c) Perfect Square(d) Prime NumberI got this question in exam.My question is based upon Patterns in Squares topic in section Squares and Square Roots of Mathematics – Class 8

Answer»

The CORRECT CHOICE is (c) Perfect Square

To elaborate: If we combine two CONSECUTIVE triangular numbers, we get a square number, like

1 + 3 = 4 = 2^2 HENCE, we get a perfect square when we add two consecutive triangular numbers. Here options other than Perfect Square are incorrect.
Discussion
56.

There are ______ non-squares numbers in between 5^2 & 6^2.(a) 10(b) 11(c) 12(d) 9This question was posed to me in semester exam.My question is taken from Patterns in Squares in division Squares and Square Roots of Mathematics – Class 8

Answer» RIGHT choice is (a) 10

Easy explanation: The squares of the numbers 5 & 6 are 25 & 36 RESPECTIVELY. There are 10 numbers between 25 and 36 (i.e. 26, 27, 28, 29, 30, 31, 32, 33, 34, 35). THEREFORE, the correct answer would be 10 and the others would be incorrect.
Discussion
57.

_____ is a triangular number.(a) 3(b) 2(c) 5(d) 7The question was posed to me by my school teacher while I was bunking the class.My doubt stems from Patterns in Squares topic in section Squares and Square Roots of Mathematics – Class 8

Answer»

Right option is (a) 3

The EXPLANATION: Triangular numbers are the numbers which when ARRANGED in increasing order forms shape of triangle. Here, 3 is the only triangular number. Hence, 3 is the correct answer and OTHERS are incorrect.
Discussion
58.

What are triangular numbers?(a) The numbers whose dot pattern can be arranged in triangles(b) The numbers which form a triangle on adding(c) The numbers which have three digits(d) The numbers which do not give perfect squares on addingThe question was posed to me during an internship interview.This intriguing question comes from Patterns in Squares in chapter Squares and Square Roots of Mathematics – Class 8

Answer»

The correct ANSWER is (a) The NUMBERS whose dot pattern can be arranged in triangles

Explanation: Triangular numbers are the numbers which when arranged in increasing order forms a shape of TRIANGLE, the triangle SHOWN below represents the number 6.
Discussion
59.

If square of 11 is 121 then, what is the square of 111?(a) 121(b) 12321(c) 1234321(d) 123321The question was posed to me in an international level competition.This key question is from Properties of Squares topic in section Squares and Square Roots of Mathematics – Class 8

Answer»

The correct answer is (b) 12321

The explanation is: The SQUARES of the numbers containing one on all places show a very BEAUTIFUL pattern.

The pattern is as FOLLOWS, 11^2=121 => 111^2=12321. HENCE students can use this pattern to CALCULATE the squares of all the numbers having 1 on it’s all places.
Discussion
60.

How can one express 144 in terms of squares?(a) 12^2-1(b) 144-1(c) 13^2-1(d) 142+1The question was asked in unit test.Enquiry is from Properties of Squares in portion Squares and Square Roots of Mathematics – Class 8

Answer»

Right ANSWER is (a) 12^2-1

To elaborate: Here all the options other then 13^2-1 GIVE 143 as their answer but only 12^2-1 gives

it in the form of squares. Hence the CORRECT answer would be 12^2-1.
Discussion
61.

If we add the first n odd numbers we get ______(a) n^2(b) 2n(c) 3n(d) nThe question was posed to me in a job interview.My enquiry is from Properties of Squares in portion Squares and Square Roots of Mathematics – Class 8

Answer»

Correct CHOICE is (a) n^2

To explain: When we add FIRST n odd NUMBERS we get, n^2.

For example: the first 5 odd numbers are 1, 3, 5, 7 and 9

When we add them, we get, 1+3+5+7+9+=25. We know that 25 is the square of number 5. HENCE, we find that when first n numbers are added we get n^2.
Discussion
62.

There are _____ non-square numbers between square of 5 and 6.(a) 11(b) 12(c) 13(d) 10The question was posed to me in an interview for internship.The query is from Properties of Squares in portion Squares and Square Roots of Mathematics – Class 8

Answer»

Correct option is (d) 10

To elaborate: The non-square numbers are the number which aren’t PERFECT squares, therefore the numbers between the square of 5 and 6 (i.e. 25 and 36) is 10 the numbers are 26, 27, 28, 29, 30, 31, 32, 33, 34 and 35.
Discussion
63.

If we add two triangular numbers what would be the result?(a) Square(b) Square Root(c) Cube(d) Cube RootThe question was asked by my school teacher while I was bunking the class.Query is from Properties of Squares topic in portion Squares and Square Roots of Mathematics – Class 8

Answer»

Right OPTION is (a) Square

Explanation: If we add TWO triangular numbers then the SUM would be a perfect square.

For example: 1 and 3 are triangular number when added to each other GIVES 4, 4 is a perfect square.
Discussion
64.

Which of the following cannot be a square of the number of with 4 at it’s one’s place?(a) 4(b) 196(c) 36(d) 144This question was posed to me in an interview for internship.My question comes from Properties of Squares in portion Squares and Square Roots of Mathematics – Class 8

Answer»

Right ANSWER is (B) 196

Explanation: We know that the number which has 4 in it’s one’s place has it’s ending with 6 in it’s one’s place. Here 36 cannot be the CORRECT answer SINCE it is square of 6. Here the correct answer is 196 as it is square of 14.
Discussion
65.

If a number has 1 in it’s one’s place, what can be it’s square?(a) 91(b) 144(c) 169(d) 121This question was posed to me during an interview.Asked question is from Properties of Squares topic in division Squares and Square Roots of Mathematics – Class 8

Answer»

The correct option is (d) 121

Explanation: We know that if a NUMBER has 1 in it’s one’s place the square of that particular number would also have 1 in it’s one’s place. Here there are TWO options that can be correct but the option 91 couldn’t be correct because it isn’t a PERFECT square. THEREFORE the correct option would be 121.
Discussion
66.

Which of the following is not a triangular number?(a) 1(b) 10(c) 15(d) 20I got this question in an interview.The query is from Properties of Squares in chapter Squares and Square Roots of Mathematics – Class 8

Answer»

Right option is (d) 20

To ELABORATE: Triangular numbers are the numbers which when arranged in increasing order forms a shape of triangle. Here the options other than 20 form triangular numbers. Hence the CORRECT option would be 20, SINCE it does not form a triangular number.
Discussion
67.

Which of the following is a triangular number?(a) 2(b) 4(c) 5(d) 6This question was addressed to me during an internship interview.This intriguing question comes from Properties of Squares in section Squares and Square Roots of Mathematics – Class 8

Answer» CORRECT CHOICE is (d) 6

The BEST I can explain: Triangular numbers are the numbers which when arranged in increasing order forms a shape of triangle, the triangle shown represents the NUMBER 6. Hence the only number forming the triangular number is 6. Hence the OPTIONS other than 6 are incorrect.
Discussion
68.

________ is the square of 25.(a) 625(b) 525(c) 125(d) 655The question was asked in an interview.My question is from Properties of Squares topic in division Squares and Square Roots of Mathematics – Class 8

Answer»

Right choice is (a) 625

The explanation is: A square of any number is the product which is OBTAINED by multiplying the number with itself. So, here 25×25=625. HENCE the ANSWER WOULD be 625, and the others would be INCORRECT.
Discussion