Question

p is the smallest possible integer such that 540p is a square number. What is the value of p

Answer 1

$\sf{\pink{\underline{\underline{Given:-}}}}$

p is the smallest possible integer such that 540p is a square number.

$\sf{\blue{\underline{\underline{To\:find:-}}}}$

The value of p

$\sf{\orange{\underline{\underline{Answer:-}}}}$

On prime factorising 540 we get

• 540 = (3 * 3) * 3 * (2 * 2) * 5

These 3 and 5 which is 3*5 = 15 does not form a pair.

If we multiply 15 with 540 it will become a perfect square.

540*15 = 8100 is a perfect square.

And we know,

540* p is a perfect square.

So,

540* p = 540 * 15

Hence $\sf{\large{\red{\boxed{\boxed{p=15}}}}}$

Ans. is p=15