Algebra

Surds and Simplifying Square Roots

Write square roots in exact simplified form.

Algebra & number overviewStandard formPercentages

Main rule

\[\sqrt{ab}=\sqrt a\sqrt b\]

Choose the largest square factor so the surd becomes as simple as possible.

√72 = √(36×2)= √36 × √2= 6√2square factor
Use the largest square factor of 72, which is 36.

Worked example

Simplify \(\sqrt{98}\).

\[\sqrt{98}=\sqrt{49\times2}=7\sqrt2.\]