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.
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Surds can be simplified if the number in the surd has a square number as a factor.
Remember these general rules:
\(\sqrt{a} \times \sqrt{a} = a\)
\(\sqrt{ab} = \sqrt{a} \times \sqrt{b}\)
\(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\)
Simplify \(\sqrt{12}\).
4 is a factor of 12 so we can write \(\sqrt{12} = \sqrt{(4\times3)} = \sqrt{4}\times\sqrt{3}\)
\(\sqrt{4} = 2\) so \(\sqrt{12} = 2\sqrt{3}\)
Simplify \(\sqrt{10} \times \sqrt{5}\)
\(\sqrt{10} \times \sqrt{5} = \sqrt{50}\)
\(50 = 25 \times 2\), so we can write \(\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}\)
Simplify \(\frac{\sqrt{12}}{\sqrt{6}}\)
\(\frac{\sqrt{12}}{\sqrt{6}} = \sqrt{\frac{12}{6}} = \sqrt{2}\)
Simplify the following surds: