Rationalize the denominator of the following- 1-7-6

Multiply the numerator and denominator by(√(7)+√(6)) nbsp;. nbsp; We get, 1/√(7) √(6)=1(√(7)+√(6))/(√(7) √(6))(√(7)+√(6)) =√(7)+√(6)/(√(7))^2 (√(6))^2=√(7) ...

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Standard IX

Mathematics

Fractional Exponent

Rationalize t...

Question

Rationalize the denominator of the following:

$\frac{1}{(\sqrt{7} - \sqrt{6})}$

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Solution

Multiply the numerator and denominator by $(\sqrt{7} + \sqrt{6}) . We get, \frac{1}{\sqrt{7} - \sqrt{6}} = \frac{1 (\sqrt{7} + \sqrt{6})}{(\sqrt{7} - \sqrt{6}) (\sqrt{7} + \sqrt{6})} = \frac{\sqrt{7} + \sqrt{6}}{(\sqrt{7})^{2} - (\sqrt{6})^{2}} = \frac{\sqrt{7} + \sqrt{6}}{1} = \sqrt{7} + \sqrt{6}$
$[u s i n g t h e i d e n t i t y (a + b) (a - b) = a^{2} - b^{2}]$

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Rationalize the denominator of the following: 1(√7−√6)

Multiply the numerator and denominator by(√7+√6).We get,1√7−√6=1(√7+√6)(√7−√6)(√7+√6)=√7+√6(√7)2−(√6)2=√7+√61=√7+√6 [using the identity (a+b)(a−b)=a2−b2]

Rationalize the denominator of the following:

$\frac{1}{(\sqrt{7} - \sqrt{6})}$