Question

Find the smallest natural number by which 53240 must be divided so that the quotient is a perfect cube.Find the cube root of the new number also.

Answer 1

Answer:

10648.

Step-by-step explanation:

If we divided the number by 5, then the prime factorisation of the quotient will not contain 5. Hence the smallest number by which 53240 should be divided to make it a perfect cube is 5. The perfect cube in that case is=10648.

Answer 2

Answer:-

For finding the perfect cube you've to prime factorize 53240...

Please find the attached file... (after checking proceed)

$\sqrt[3]{53240}$ = 5 x 2 x 2 x 2 x 11 x 11 x 11

5 doesn't have a pair as it needs 2 more 5's, so the least number to divide is 5.

53240÷5 = 10648

∛10648 (Find the 2nd file attached, please)(After checking)

∛10648 = ∛2x2x2x11x11x11x11

Make trios of 2 and 11 and take 1 from each

so 11 x 2

= 22 is the cube root