Concept preview

What you will be able to do

1. 01Solve equations containing a radical by isolating and squaring
2. 02Recognise and reject extraneous roots by checking in the original equation
3. 03Apply radical equations to geometry and real-world formulas

A radical equation has the variable trapped under a square root, like $\sqrt{x} = 5$. To free it, use the fact that squaring undoes a square root: $(\sqrt{x})^2 = x$. So square both sides of $\sqrt{x} = 5$ to get $x = 25$. That is the whole strategy — but there is one crucial catch that we will meet in a moment, so read on before you trust every answer.