Examples with squares and square roots

When you need to find a subject that has been squared in your formula, you need to find the square root of each side.

If \(y={x}^2\), then \(x=\sqrt{y}\)

If \(y={x}^2 + 3\), then \({x}^2=y-3\), so \(x=\sqrt{y-3}\)

When you need to find a subject that is contained by a square root, you need to square each side.

If \(y=\sqrt{x}\), then \(x={y}^2\)

If \(y=\sqrt{x}+3\), then \(\sqrt{x}=y-3\), so \(x=(y-3)^2\)

Now try the example questions below.

Question

Using the formula for the area of a circle, change the subject of the formula to 'r'.

Change the subject of the formula \(E_k = \frac{1}{2}m{v^2}\) to \(v\)