Question

10. Is 292 a perfect cube ? If not , find the smallest natural number by which it must be multiplied so that the product is a perfect cube .​

Answer 1

${\underline{\underline{\bf{Solution-}}}}$

To Find :

To find whether 292 is a perfect cube or not, To find the smallest natural number by which it must be multipiled so that the product is a perfect cube.

292 = 2 x 2 x 73 , which doesn't have triplet of any prime factors,

Hence, to make it perfect cube, we must make the the prime factors to form triplets,.

292 x 2 x 73 x73 = 2 x 2 x 2 x 73 x 73 x 73

=> Hence, it should be multiplied by 2 x 73 x 73 = 5329 x 2 = 10658.

Answer 2

Answer: no, it was not perfect cube 73 should be multiplied

Step-by-step explanation:

no 292 is not a perfect cube

292 = 2×2×73

so, another 73 should be multiplied with 292 to make ita perfect square