sqrt(x) = 3 sqrt(x)

or

sqrt(x) = cbrt(x) where ‘cbrt’ denotes ‘cube root’?

In the first case, square the equation.

x = 9x

9x – x = 0

8x = 0

x = 0.

When you square an equation you must always check the results, as squaring can introduce extra solutions which may not be valid. x = 0 is all right.

sqrt(x) = cbrt(x)

Raise each side to the 6th power:

x^3 = x^2

x^3 – x^2 = 0

x^2(x – 1) = 0

x = 0 or x = 1.

Both roots check out.

Raising each side to the 6th power we shall get

x^3 = x^2

x^3 – x^2 = 0

x^2(x – 1) = 0

x = 0 or x = 1.

If so, 0 and 1 can be solutions of this one…

the square root of 0 equals the cube root of 0 – both equal 0

and

the square root of 1 equals the cube root of 1 – both equal 1