Mathematics » Roots and Radicals » Simplify and Use Square Roots

# Simplifying and Using Square Roots Summary

## Key Concepts

• Note that the square root of a negative number is not a real number.
• Every positive number has two square roots, one positive and one negative. The positive square root of a positive number is the principal square root.
• We can estimate square roots using nearby perfect squares.
• We can approximate square roots using a calculator.
• When we use the radical sign to take the square root of a variable expression, we should specify that $$x\ge 0$$ to make sure we get the principal square root.

## Glossary

### square of a number

• If $${n}^{2}=m$$, then $$m$$ is the square of $$n$$

### square root of a number

• If $${n}^{2}=m$$, then $$n$$ is a square root of $$m$$

### square root notation

• If $$m={n}^{2}$$, then $$\sqrt{m}=n$$. We read $$\sqrt{m}$$ as ‘the square root of $$m$$.’

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