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.


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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