Question

find the rationalisation factor of 3- root5

Answer 1

Answer:

The rationalisation factor of $3 - \sqrt{5}$ is $=3 + \sqrt{5}$

Step-by-step explanation:

$3 - \sqrt{5}$

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

$=\frac{(3)^2 - (\sqrt{5})^2}{(3 + \sqrt{5})}$  [using the identity $a^2 - b^2 = (a + b)(a - b)$]

$=\frac{9 - 5}{(3 + \sqrt{5})}$

$=\frac{4}{(3 + \sqrt{5})}$

Therefore, the rationalisation factor of $3 - \sqrt{5}$ is $=3 + \sqrt{5}$