Question

Rationalize the denominator...
please let me know the answer..​

Answer 1

$\bf\huge\underline{\underline{ answer :- }}$

• $\bf \frac{2}{ \sqrt{1} - \sqrt{2} } = \frac{2}{1 - \sqrt{2} }$

• $\\ \bf = \frac{2}{1 - \sqrt{2} } \times \frac{1 + \sqrt{2} }{1 + \sqrt{2} }$

[ multiplying numerator and denominator by 1 + √2 ]

• $\\ \bf = \frac{2(1 + \sqrt{2)} }{(1 + \sqrt{2} )(1 - \sqrt{2} )}$

• $\\ \bf = \frac{2 - 2 \sqrt{2} }{1 {}^{2} - ( { \sqrt{2} })^{2}}$ [ (a+b)(a-b) = a² - b² ]

• $\\ \bf = \frac{2 - 2 \sqrt{2} }{1 - 2}$

• $\\ \bf = \frac{2 - 2 \sqrt{2} }{ - 1}$

• $\\ \bf = - (2 - 2 \sqrt{2} )$

• $\\ \boxed{ \bf = - 2 + \sqrt{2} }$