Question

When x is a perfect square, what is true about the cube of x

Answer 1

We are given x is a perfect square.

Let us take x in terms of another variable p.

Let us assume square root of x gives a value p (because x is a perfect square, square root of x would give a perfect number).

`√(x) = p`

Squaring both sides, we get

`(√(x))^2= (p)^2`

Square cancels a square root, so we get only x on left side.

`x=p^2`

We need to find the value of x cube.

Taking cube on both sides, we get

`(x)^3 = (p^2)^3`

Applying power of power rule of exponents (we multiply power of power).

`x^3 = p^6`

We can see p^6 is also a perfect square.

So, we could say x^3 is also a perfect square.