Question

what should be multiplied to 288 to become a perfect square?​

Answer 1

Answer:

Should be multiplied by 2

Step-by-step explanation:

First find Lcm of 288:

2 | 288

2 | 144

2 | 72

2 | 36

2 | 18

3 | 9

3 | 3

1

so, (2 x 2),(2 x 2),(3 x 3)

2 is left out in pair so  288 x 2 = 576

square root of 576 = 24

Hence 288 should be multiplied with 2 to get a perfect square

Answer 2

Step-by-step explanation:

Given that:what should be multiplied to 288 to become a perfect square?

To find: The number ,which after multiplication convert 288 in perfect square

Solution:

To find that number ,

Do prime factorisation of 288

$288 = 2 \times 2 \times 2 \times 2 \times \times 3 \times 3 \\ \\ 288 = {2}^{5} \times {3}^{2}$

It is clear that if 2 has Exponent of multiple of 2,the number will become a perfect square.

It should be multiplied by 2,so that

$288 \times 2= {2}^{6} \times {3}^{2} \\ \\ \sqrt{576} = \sqrt{ {( {2}^{3} \times 3) }^{2} } \\ \\ \sqrt{576} = {2}^{3} \times 3 \\ \\ \sqrt{576} = 24$

Thus,

The least number which is multiplied to 288 to become it a perfect square is 2.

Hope it helps you.