Answer
In a fraction to rationalize denominator means to replace an irrational number by a rational number in the denominator without changing the value of the fraction.
Explanation
a). Rationalizing the denominator of $\frac{1}{\sqrt 5}$ = $\frac{\sqrt 5}{ 5}$
b). a). Rationalizing the denominator of $\frac{1}{5 + \sqrt 5}$ = $\frac{{(5 - \sqrt 5)}}{{20}}$
Work Step by Step
In a fraction to rationalize denominator means to replace irrational number by rational number in denominator without changing the value of fraction.
Explanation
a). Rationalizing the denominator of $\frac{1}{\sqrt 5}$ = . $\frac{1\times{\sqrt 5}}{\sqrt 5\times{\sqrt 5}}$ = $\frac{\sqrt 5}{ 5}$
b). a). Rationalizing the denominator of $\frac{1}{5 + \sqrt 5}$
multiply both nominator and denominator by complex conjugate of $(5 + \sqrt 5)$ = $(5 - \sqrt 5)$
= . $\frac{1\times{(5 - \sqrt 5)}}{(5 + \sqrt 5)\times{(5 - \sqrt 5)}}$
= $\frac{{(5 - \sqrt 5)}}{(5 + \sqrt 5)\times{(5 - \sqrt 5)}}$
by formula ${(a + b){(a - b)}}$ = $a^{2} - b^{2}$
$\frac{{(5 - \sqrt 5)}}{(5 + \sqrt 5)\times{(5 - \sqrt 5)}}$
= $\frac{{(5 - \sqrt 5)}}{5^{2} - \sqrt 5^{2}}$
= $\frac{{(5 - \sqrt 5)}}{{25} - {5}}$
= $\frac{{(5 - \sqrt 5)}}{{20}}$
