How do you simplify (5 + sqrt 3) /( 2 - sqrt3)?

Apr 11, 2016

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

Explanation:

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

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

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

$\frac{5 + \sqrt{3}}{2 - \sqrt{3}} \times \frac{2 + \sqrt{3}}{2 + \sqrt{3}} \text{ "=" } \frac{\left(5 + \sqrt{3}\right) \left(2 + \sqrt{3}\right)}{{2}^{2} - \left[{\left(\sqrt{3}\right)}^{2}\right]}$

$\implies \frac{10 + 5 \sqrt{3} + 2 \sqrt{3} + 3}{4 - 3}$

$\implies 13 + 7 \sqrt{3}$