How do you simplify $\frac{5 + \sqrt{3}}{2 - \sqrt{3}}$ $(5 + sqrt 3) /( 2 - sqrt3)$ ?

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How do you simplify $\frac{5 + \sqrt{3}}{2 - \sqrt{3}}$ $(5 + sqrt 3) /( 2 - sqrt3)$ ?

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Answer 1 · 2016-04-11T14:21:35

$\frac{5 + \sqrt{3}}{2 - \sqrt{3}} = 13 + 7 \sqrt{3}$ $(5+sqrt(3))/(2-sqrt(3))=13+7sqrt(3)$

Explanation:

Using $a^{2} - b^{2} = (a + b) (a - b)$ $a^2-b^2=(a+b)(a-b)$

You can write the value 1 in many ways: $\frac{2}{2}; \frac{16}{16}; or 1 = \frac{2 + \sqrt{3}}{2 + \sqrt{3}}$ $2/2; 16/16; or 1=(2+sqrt(3))/(2+sqrt(3))$

Multiply by 1 but in the form $1 = \frac{2 + \sqrt{3}}{2 + \sqrt{3}}$ $1=(2+sqrt(3))/(2+sqrt(3))$ giving

$\frac{5 + \sqrt{3}}{2 - \sqrt{3}} \times \frac{2 + \sqrt{3}}{2 + \sqrt{3}} = \frac{(5 + \sqrt{3}) (2 + \sqrt{3})}{2^{2} - [{(\sqrt{3})}^{2}]}$ $(5+sqrt(3))/(2-sqrt(3)) xx (2+sqrt(3))/(2+sqrt(3))" "=" "( (5+sqrt(3))(2+sqrt(3)))/(2^2 -[(sqrt(3))^2])$

$\Rightarrow \frac{10 + 5 \sqrt{3} + 2 \sqrt{3} + 3}{4 - 3}$ $=> (10+5sqrt(3)+2sqrt(3)+3)/(4-3)$

$\Rightarrow 13 + 7 \sqrt{3}$ $=>13+7sqrt(3)$

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