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1.

Find the cube root of 17576 through estimation.

Answer» 17576
`20^3<17576<30^3`
Unit digit of 17576 is 6
unit digit will be 6
`17576=26`
Discussion
2.

Is 68600 a perfect cube? If not, find the smallest number by which 68600 must be multiplied to get a perfect cube.

Answer» LCM(68600)=2*2*2*5*5*7*7*7
No, it is not a perfect cube
after multiplying by 5 this number can be a perfect cube.
Discussion
3.

State true or false.(i)        Cube of any odd number is even.(ii)       A perfect cube does not end with two zeros.(iii)      If square of a number ends with 5, then its cube ends with 25.(iv)      There is no perfect cube which ends with 8.(v)       The cube of a two digit number may be a three digit number.(vi)      The cube of a two digit number may have seven or more digits.(vii)     The cube of a single digit number may be a single digit number.

Answer» (a) false(product of odd numbers is odd)
(b)True
(c)false
(d)false
(e)false
(f)false
(g)true
Discussion
4.

You are told that 1,331 is a perfect cube. Can you guess without factorisation what is its cube root? Similarly, guess the cube roots of 4913, 12167, 32768.

Answer» 1) 1331
`10^3<1331<20^3`
`1331=11^3`
2)4913
`10^3<4913<20^3`
`4913=17^3`
3)12167
`20^3<12167<30^3`
`12167=23^3`4)32768
`30^3<32768<40^3`
`32768=32^3`.
Discussion
5.

Is 243 a perfect cube?

Answer» LCM(243)=3*3*3*3*3
3 is not in a triplet
243 is not perfect cube.
Discussion
6.

Is 53240 a perfect cube? If not, then by which smallest natural number should 53240 be divided so that the quotient is a perfect cube?

Answer» `53240 = 2**2**2**5**11**11**11 =2^3**11^3**5`
Thus, `53240` is not a perfect cube.
If we divide it by `5` it will a perfect cube.
Discussion
7.

Is 392 a perfect cube? If not, find the smallest natural number by which 392 must be multiplied so that the product is a perfect cube.

Answer» LCM(392)=2*2*2*7*7
No, this is not a perfect cube.
after multiplying by 7 we can make it perfect cube
new number=392*7=2744.
Discussion
8.

Is 1188 a perfect cube? If not, by which smallest natural number should 1188 be divided so that the quotient is a perfect cube?

Answer» `1188 = 11**3**3**3**2**2`
Thus, `1188` is not a perfect cube.
If we divide it by `44(11**2**2)` it will be a perfect cube.
Discussion