Question

# Rationalise the denominator of each of the following: $\frac{\sqrt{3}-1}{\sqrt{3}+1}$

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Solution

## On multiplying the numerator and denominator of the given number by $\sqrt{3}-1$, we get: $\frac{\sqrt{3}-1}{\sqrt{3}+1}=\frac{\sqrt{3}-1}{\sqrt{3}+1}×\frac{\sqrt{3}-1}{\sqrt{3}-1}\phantom{\rule{0ex}{0ex}}=\frac{{\left(\sqrt{3}-1\right)}^{2}}{{\left(\sqrt{3}\right)}^{2}-{\left(1\right)}^{2}}\phantom{\rule{0ex}{0ex}}=\frac{3+1-2\sqrt{3}}{3-1}\phantom{\rule{0ex}{0ex}}=\frac{4-2\sqrt{3}}{2}\phantom{\rule{0ex}{0ex}}=\frac{2\left(2-\sqrt{3\right)}}{2}\phantom{\rule{0ex}{0ex}}=2-\sqrt{3}$

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