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).
[tex]\sqrt{x} = p[/tex]
Squaring both sides, we get
[tex](\sqrt{x})^2= (p)^2[/tex]
Square cancels a square root, so we get only x on left side.
[tex]x=p^2[/tex]
We need to find the value of x cube.
Taking cube on both sides, we get
[tex](x)^3 = (p^2)^3[/tex]
Applying power of power rule of exponents (we multiply power of power).
[tex]x^3 = p^6[/tex]
We can see p^6 is also a perfect square.
So, we could say x^3 is also a perfect square.
