Question

-7/ROOT11 -ROOT 5 HOW TO SOLVE THIS QUE RATIONALISATION

Answer 1

Step-by-step explanation:

Here, we have to rationalise the denominator of,

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

In order to rationalise the denominator of any fraction, we multiply the rationalising factor of the denominator with both the numerator and the denominator of the fraction.

Rationalising factor is also the conjugate of the denominator. Rationalising factor of (a - b) is (a + b). So, the rationalising factor of (√11 - 5) is (√11 + 5).

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

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, rationalised!