Question

Rationalize the denominator 1 upon 5 + root 3​

Answer 1

Step-by-step explanation:

.

$\frac{1}{5 + \sqrt{3} }$

$multiply \: and \: divide \: by \: 5 - \sqrt{3}$

$= > \frac{1}{5 + \sqrt{3} } \times \frac{5 - \sqrt{3} }{5 - \sqrt{3} }$

$= > \frac{5 - \sqrt{3} }{(5 + \sqrt{3)(5 - \sqrt{3} )} }$

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

$= > \frac{5 - \sqrt{3} }{ {5}^{2} - { (\sqrt{3}) }^{2} }$

$= > \frac{5 - \sqrt{3} }{25 - 3}$

$= > \frac{5 - \sqrt{3} }{22}$