Question

Rationalise the denominator of: -7/(√11 - √5)​

Answer 1

$\sf \underline{ \red{Solution - }}$

Given,

$\sf{\quad { \dfrac{-7}{\sqrt{11} - \sqrt{5}} }}$

The denominator is √11 - √5.

We know that

Rationalising factor of √a-√b is √a+√b.

Therefore, the rationalising factor of √11-√5 is √11+√5.

On rationalising the denominator them

$\longrightarrow \sf{\quad { \dfrac{-7}{\sqrt{11} - \sqrt{5}} \times \dfrac{(\sqrt{11} + \sqrt{5})}{(\sqrt{11} + \sqrt{5})} }}$

Multiplying (√11 + √5) with both the numerator of the fraction.

$\longrightarrow \sf{\quad { \dfrac{-7(\sqrt{11} + \sqrt{5}) }{(\sqrt{11} - \sqrt{5})(\sqrt{11} + \sqrt{5})} }}$

Performing multiplication in the numerator and by using identity (a + b)(a - b) = a² - b², solving further in the denominator.

$\longrightarrow \sf{\quad { \dfrac{-7\sqrt{11} -7\sqrt{5}}{(\sqrt{11})^2 - (\sqrt{5})^2} }}$

Writing the squares of the numbers in the denominator.

$\longrightarrow \sf{\quad { \dfrac{-7\sqrt{11} -7\sqrt{5}}{11 -5} }}$

Performing subtraction in the denominator.

$\longrightarrow \quad \underline{ \boxed{ \dfrac{ \textbf{ \textsf{-7 }}\sqrt{ \textbf{ \textsf{11 }}} - \textbf{ \textsf{7}}\sqrt{ \textbf{ \textsf{5 }}}}{ \textbf{ \textsf{ 6}}}} }$

Hence, the denominator is rationalised.

Answer 2

-7(sqrt(11)+sqrt(5))/6


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