Question

Write 540 as the product of its prime factors.
p is the smallest possible integer such that 540p is a square number.
Find
$\sqrt{540p}$
540p, giving your answer as the product of its prime factors.​

Answer 1

Answer:

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

The value of p

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  

Ans. is p=15