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Rational and Irrational Numbers — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSRational and Irrational Numbers2 Marks
Question
Rationalise the denominators of : $\frac{\sqrt{3}+1}{\sqrt{3}-1}$
✓

Answer

$ \frac{\sqrt{3}+1}{\sqrt{3}-1} \times \frac{\sqrt{3}+1}{\sqrt{3}+1}$
$= \frac{(\sqrt{3}+1)^2}{(\sqrt{3})^3-(1)^2}$
$= \frac{3+1+2 \sqrt{3}}{3-1}$
$= \frac{4+2 \sqrt{3}}{2}$
$= \frac{2(2+\sqrt{3})}{2}$
$= 2+\sqrt{3}$

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