Question

1. Rationalise the denominator
14/(5
$\sqrt{3} - \sqrt{5}$




​

Answer 1

Answer :

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

Step-by-step explanation :

$\underline{\underline{\textbf{Rationalizing factor :}}}$

      $\bigstar$  The factor of multiplication by which rationalization is done, is called as rationalizing factor.

      $\bigstar$  If the product of two surds is a rational number, then each surd is a rationalizing factor to other.

      $\bigstar$  For example, rationalizing factor of (3 + √2) is (3 - √2)

_______________________________________

$=\frac{14}{5\sqrt{3}-\sqrt{5}}$

Rationalizing factor = 5√3 + √5

$\bf{=\frac{14}{5\sqrt{3}-\sqrt{5}} \times \frac{5\sqrt{3}+\sqrt{5}}{5\sqrt{3}+\sqrt{5}} }\\\\\\ = \frac{14(5\sqrt{3}+\sqrt{5})}{(5\sqrt{3}-\sqrt{5})(5\sqrt{3}+\sqrt{5})} \\\\\\ =\frac{14(5\sqrt{3}+\sqrt{5})}{(5\sqrt{3})^2-\sqrt{5}^2} \\\\\\ =\frac{14(5\sqrt{3}+\sqrt{5})}{25(3)-5} \\\\\\ =\frac{14(5\sqrt{3}+\sqrt{5})}{75-5} \\\\\\ =\frac{14(5\sqrt{3}+\sqrt{5})}{70} \\\\\\ =\frac{14(5\sqrt{3}+\sqrt{5})}{14(5)} \\\\\\ =\frac{5\sqrt{3}+\sqrt{5}}{5} \\\\\\ =\sqrt{3} +\frac{1}{5} \sqrt{5}$

Answer 2

Hope my answer Helps to u

..........