National 5

Working with surdsRules of surds

Surds are square roots which can’t be reduced to rational numbers. Some can be simplified using various rules or by rationalising the denominator.

Part ofMathsNumerical skills

Rules of surds

Remember that there are three simple rules of surds:

	Rules of surds
1	\(\sqrt a \times \sqrt a = a\)
2	\(\sqrt {ab} = \sqrt a \times \sqrt b\)
3	\(\sqrt {\frac{a}{b}} = \frac{{\sqrt a }}{{\sqrt b }}\)

	1
Rules of surds	\(\sqrt a \times \sqrt a = a\)

	2
Rules of surds	\(\sqrt {ab} = \sqrt a \times \sqrt b\)

	3
Rules of surds	\(\sqrt {\frac{a}{b}} = \frac{{\sqrt a }}{{\sqrt b }}\)

Test your understanding

Rationalising the denominator

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