How do you rationalize the denominator and simplify $\frac{2 + \sqrt{2}}{\sqrt{3}}$ $(2+sqrt2)/sqrt3$ ?

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How do you rationalize the denominator and simplify $\frac{2 + \sqrt{2}}{\sqrt{3}}$ $(2+sqrt2)/sqrt3$ ?

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Answer 1 · 2017-08-02T08:49:25

$\frac{2 \sqrt{3} + \sqrt{6}}{3}$ $(2sqrt3+sqrt6)/3$

Explanation:

$to rationalise the denominator$ $"to rationalise the denominator"$

$multiply the numerator/denominator by \sqrt{3}$ $"multiply the numerator/denominator by " sqrt3$

$∙ x \sqrt{a} \times \sqrt{a} = a$ $•color(white)(x)sqrtaxxsqrta=a$

$∙ x \sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$ $•color(white)(x)sqrtaxxsqrtb=sqrt(axxb)$

$\Rightarrow \frac{2 + \sqrt{2}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$ $rArr(2+sqrt2)/sqrt3xxsqrt3/sqrt3$

$= \frac{\sqrt{3} (2 + \sqrt{2})}{3} \leftarrow rational denominator$ $=(sqrt3(2+sqrt2))/3larrcolor(red)" rational denominator"$

$= \frac{2 \sqrt{3} + \sqrt{6}}{3}$ $=(2sqrt3+sqrt6)/3$

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How do you rationalize the denominator and simplify $\frac{2 + \sqrt{2}}{\sqrt{3}}$ $(2+sqrt2)/sqrt3$ ?

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How do you rationalize the denominator and simplify $\frac{2 + \sqrt{2}}{\sqrt{3}}$ $(2+sqrt2)/sqrt3$ ?