Question

find the smallest number by which 7688 must be multiplied so that the product is a perfect cube

Answer 1

Question :- Find the smallest number by which 7688 must be multiplied so that the product is a perfect cube.



Answer :-

Firstly, we will find the prime factors of 7688

7688 = 2 × 2 × 2 × 31 × 31

Prime factors of 7688 are 2 × 2 × 2 × 31 × 31

Here, only 31 is not in cube. 2 is in cube form.



∴ The smallest number by which 7688 must be multiplied so that the product is a perfect cube is 31




Let's check ✔

7688 × 31

=> 238328

$^{3}\sqrt{238328}$ = 62 ✔✔

Answer 2

Answer:

31

Step-by-step explanation:

We have to find a number which on being multiplied by 7688, gives a perfect cube.

First of all, we have to calculate the prime factors of the given number i.e. 7688,

Prime factors of 7688 = 2 * 2 * 2 * 31 * 31 = 2³ * 31²

We know that for being a perfect cube, the prime factors of the number should be in the cube and here we see that ( 2 ) is raised to the power three but ( 31 ) is raised to the power 2 only!

Therefore,

7688 must be multiplied by 31 to get a perfect cube.

Verification:

7688 * 31 = 238328

∛238328 = ∛( 2³ * 31³)

∛238328 = 2 * 31

∛238328 = 62