Question

raitionlize the denominator of the following
3/√3+√5-√2​

Answer 1

To Rationalize:

$\dfrac{3}{ \sqrt{3} + \sqrt{5} - \sqrt{2}}$

Solution:

$= \dfrac{3}{ \sqrt{3} + \sqrt{5} - \sqrt{2}} \\ \\ = \frac{3}{ \sqrt{3} - \sqrt{2} + \sqrt{5} } \\ \\ = \frac{3}{ \sqrt{3} - \sqrt{2} + \sqrt{5}} \times \frac{ \sqrt{3} - \sqrt{2} - \sqrt{5}}{\sqrt{3} - \sqrt{2} - \sqrt{5} }\\ \\ = \frac{3(\sqrt{3} - \sqrt{2} - \sqrt{5})}{ {( \sqrt{3} - \sqrt{2})}^{2} - {( \sqrt{5})}^{2} } \\ \\ = \frac{3(\sqrt{3} - \sqrt{2} - \sqrt{5})}{ 3 - 2. \sqrt{3}. \sqrt{2} + 2 - 5} \\ \\ = \frac{3(\sqrt{3} - \sqrt{2} - \sqrt{5})}{5 - 5 - 2\sqrt{6} } \\ \\ = \boxed{ - \frac{3( \sqrt{3} - \sqrt{2} - \sqrt{5})}{2 \sqrt{6} } }$

Algebra Formula Used

a² - b² = (a+b)(a-b)

(a - b)² = a² - 2ab + b²

Extra Information

Rationalizing the denominator is a process by which we can write the irrational denominator in the form of Rational no.

For Rationalizing we use a Conjugate surds or Rationalizing factor which is a factor of the irrational denominator.

e.g conjugate surd of √a is √a and the conjugate surds √a - b is √a + b.