Square roots

What it looks like

√ is the square root spell. It undoes a square.

√25 asks: what number times itself makes 25? The answer is 5.

This spell needs no number. You just cast it.

Worked example 1

1. x² = 25

2. √ Apply square root to both sides

3. x = 5

Check it: 5 times 5 is 25. It works.

Worked example 2

1. 3x² = 75

2. ÷ Divide both sides by 3

3. x² = 25

4. √ Apply square root to both sides

5. x = 5

Divide first. If you try the square root spell on 3x², the wizard stops you. He says, "The square root spell needs a pure square to work on — simplify first!"

The most common mistake

Thinking square root means "half".

Good to know

The game always uses the answer that is above zero. Older players may know that −5 times −5 is also 25.