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$\frac{\sqrt5 -2\sqrt3}{\sqrt2 + \sqrt{12}}$ is expression in surd form

$\frac{\sqrt5 -2\sqrt3}{\sqrt2 + \sqrt{12}}$ is expression in surd form
i) Write down the conjugate of the denominator in its simplest form
ii) Hence use the conjugate in (i) above to rationalize the denominator in the expression above

Answers

John
i) The conjugate of the denominator in simplest form

= $\sqrt2 \; - \sqrt12 \; = \; \sqrt2 \; - \; \sqrt{4\times 3}$

= $\sqrt2 -2\sqrt3$

ii) $\frac{(\sqrt5 \; 2\sqrt3)}{(\sqrt2 \; 2\sqrt3)}$ x $\frac{(\sqrt2 \; -2\sqrt3)}{(\sqrt2 \; 2\sqrt3)}$

$\frac{\sqrt{10} - 2\sqrt{15} - 2\sqrt6 \; + 4\times 3}{2\; 2\sqrt6 + 2\sqrt6 - 4 x 3}$

$\frac{\sqrt{10}\; 2\sqrt{15} \; 2\sqrt6 \; 12}{-10}$
johnmulu answered the question on March 7, 2017 at 06:12

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