Question

Find the smallest number by which 2250 must be multiplied so that the product is a perfect cube

Answer 1

Find the prime factors:

2250 = 2 x 3² x 5³

Define k:

let the number that is needed to be multiplied to 2250 to make it into a perfect cube be k.

Solve k:

2250 = 2 x 3² x 5³

2250k = 2³ x 3³ x 5³

k = 2² x 3 = 12

Answer: k = 12

Answer 2

Answer:

The smallest number is 12

Step-by-step explanation:

Given Problem:

Find the smallest number by which 2250 must be multiplied so that the product is a perfect cube​.

Solution:

To Find:

Find the smallest number.

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Method:

First we have to find the prime factors:

2250 = 2 x 3² x 5³

Let the smallest  number be x

⇒2250 = 2 x 3² x 5³

⇒2250x = 2³ x 3³ x 5³

⇒x = 2² × 3 = 12

Hence, the smallest number is 12