Question

Ratiolise the dominators
1/√7-√6​

Answer 1

Step-by-step explanation:

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

$= \frac{1}{ \sqrt{7} - \sqrt{6} } \times \frac{ \sqrt{7} + \sqrt{6} }{ \sqrt{7} + \sqrt{6} }$

$= \frac{ \sqrt{7} + \sqrt{6} }{7 - 6}$

$= \sqrt{7} + \sqrt{6}$

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Answer 2

Given : $\dfrac{1}{\sqrt {7} - \sqrt {6}}$

Need To Rationalise : The Denominator of $\dfrac{1}{\sqrt {7} - \sqrt {6}}$

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$\qquad \qquad \sf{ \star \dfrac{1}{\sqrt {7} - \sqrt {6}}}$

⠀⠀⠀⠀⠀For Rationalizing the given Denominator we have to multiply Both Numerator and Denominator by $\sqrt {7} + \sqrt {6}$ :

⠀⠀⠀⠀⠀⠀$\underline {\bf{\:Now \: By \: Multiplying \: both\: [Numerator \:and\: Denominator] \::}}$

$\qquad \qquad:\implies \sf{ \dfrac{1}{\sqrt {7} - \sqrt {6}}}$

$\qquad \qquad:\implies \sf{ \dfrac{1}{\sqrt {7} - \sqrt {6}} \dfrac{\sqrt{7}+\sqrt{6}}{\sqrt{7}+\sqrt{6}}}$

$\qquad \qquad:\implies \sf{ \dfrac{\sqrt{7}+ \sqrt{6}}{7 -6}}$

$\qquad \qquad:\implies \sf{ \dfrac{\sqrt{7}+ \sqrt{6}}{1}}$

Or,

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  Answer = \sqrt {7}+ \sqrt {6}\: }}}}\:\bf{\bigstar}$

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Therefore,

⠀⠀⠀⠀⠀$\underline {\therefore\:{ \mathrm {  By \:Rationalizing \:we \:get\:\bf{ \sqrt {7}+ \sqrt {6}\:\: }}}}$

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