Question

Find the smallest value of k such that 3240k is a perfect cube

Answer 1

Step-by-step explanation:

as3240=3^4×2^3×5,to make acube we need to make it as 3^6×2^3×5^3,so,the answer is 3^2×5^2=9×25=225

Answer 2

Given:

3240k is a perfect cube.

To Find:

The smallest possible value of k.

Solution

Find the prime factors of 3240:

3240 =  2 x 2 x 2 x 3 x 3 x 3 x 3 x 5

3240 = 2³ x 3⁴ x 5¹

Find the value of k:

Perfect cube ⇒ the exponents must be in multiples of  3

3240 = 2³ x 3⁴ x 5¹

3240k = 2³ x 3⁶ x 5³

⇒ k = 3² x 5²

⇒ k = 9 x 25

⇒ k = 225

Answer: k = 225

Check:

3240k = 3240 x 225

3240k = 729000

√3240k = √729000

√3240k = 90