Surds - AQAMultiplying out brackets including surds - Higher

Surds are numbers left in square root form that are used when detailed accuracy is required in a calculation. They are numbers which, when written in decimal form, would go on forever.

Part ofMathsNumber

Multiplying out brackets including surds - Higher

Expressions with brackets that include surds can be multiplied out or expanded.

Multiply out \((2 + \sqrt{5}) (3 + \sqrt{2})\)

Each term in the first bracket has to be multiplied by each term in the second bracket. One way to do this is to use a grid:

A grid that has simplified (3 + √2)(2 + √5)

The four terms cannot be simplified because each of the surds has a different number inside the square root, and none of the surds can be simplified.

\((2 + \sqrt{5})(3 + \sqrt{2}) = 6 + 2\sqrt{2} + 3\sqrt{5} + \sqrt{10}\)

The same method can be used if the numbers in the surds are the same:

Simplify fully \((5 - \sqrt{3})(1 + \sqrt{3})\)

Surd table showing 5 minus root 3 add 1 plus root 3

\((5 – \sqrt{3}) (1 + \sqrt{3})= 5 – \sqrt{3} + 5\sqrt{3} – 3\)

\(= 4{\sqrt{3}} + 2\)

Question

Expand \((7 + \sqrt{3})(8 + \sqrt{2})\)
Expand and simplify \((4 - \sqrt{6})(3 + \sqrt{6})\)

Rationalising denominators - Higher

Multiplying and dividing surds

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