Question

please help its urgent
3. Find the smallest number by which the following numbers must be divided so that it becomes a perfect square number.Also find the square root of resulting number
7200​​

Answer 1

$\text{\huge{\underline{\underline{AnsweR}}}}$

Given number is 7200

The prime factors of 7200:-

$\sf{7200 = 2 \times 2 \times 2 \times 2 \times 2\times 3 \times 3\times 5 \times 5}$

Organising the prime factors into pairs

$\sf{7200 = (2 \times 2) \times (2 \times 2) \times(3 \times 3) \times (5 \times 5) \times 2}$

We observe that only 2 doesnt exist in pair

So,the smallest number that should be divided from 7200 to make it a perfect square is 2

$\sf{7200 \div 2 = 3600}$

Thus the resulting number is 3600

$\sf{ \sqrt{3600} = 60}$

$\sf{\underline{\green{Therefore , \: 60 \: is \: the \: square \: root \: of \: resulting \: number \: 3600}}}$

$\mathfrak{\red{Hope\:this \:helps!!!}}$