Multiplying and dividing surds

Multiplying and dividing surds is where surds are combined using the multiplication and division rules to be written as a single surd, simplified where possible.

Surds can be multiplied or divided using the three important laws of surds, which can be derived from the laws of indices (powers) to help us to simplify surds:

√m × √n =√mn

√m ÷ √n = √m/n

√m × √m = m

Important links:

You may be asked to apply these skills at GCSE maths to give answers to problems in geometry, such as Pythagoras or trigonometry, as exact values, rather than as decimals. Before calculators were invented, surds were the standard form for stating answers which were irrational numbers.