Question

By what least number should the 3675 number be multiplied to get perfect square number also find the number whose square is the new number..

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Answer 1

Answer:

New number 11025 is the square of 105.

Step-by-step explanation:

Given number is 3675.

To get perfect square by multiplying least no.

Prime factorisation of 3675 is

3 x 5 x 5 x 7 x 7

or, 3 x 5² x 7²

So, we can see to get a perfect square we need to multiply with minimum 3.

It will give 3² x 5² x 7² which is a perfect square.

So, 3² x 5² x 7² = 11025

Hence, new no. is 11025.

so, the square root of 11025 is 3 x 5 x 7 = 105

So, 11025 is the square of 105.

Answer 2

Answer:-

Given:

The given number is 3675.

To Find:

We need to find such a number by which 3675 should be multiplied to get perfect square number also we need to find find the number whose square is the new number.

Solution:

When we find the factors of 3675, we get

3675 = 3 × 5 × 5 × 7 × 7

=> 3675 = 3 × 5^2 × 7^2

Inorder to get the perfect square we need to multiply by 3.

So, we get

3 × 3 × 5^2 ^ 7^2

= 3^2 × 5^2 × 7^2

On multiplying we get,

9 × 25 × 49

=> 225 × 49

=> 11025

$\sqrt{11025} = 3 \times 5 \times 7$

$= > \sqrt{11025} = 105$

Hence, the required number is 11025 which is the square of 105.