Question

Rationalise the denominator 8/√5-√6​

Answer 1

$\large{\underline{\underline{\mathfrak{Answer :}}}}$

The correct answer is $\sf{ 8 (\sqrt{5} + \sqrt{6})}$.

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$\large{\underline{\underline{\mathfrak{Explanation :}}}}$

As, we have to rationalise the denominator.

$\sf{\implies \dfrac{8}{\sqrt{5} - \sqrt{6}}} \\ \\ \sf{\implies \dfrac{8}{\sqrt{5} - \sqrt{6}} \times \dfrac{\sqrt{5} + \sqrt{6}}{\sqrt{5} + \sqrt{6}}} \\ \\ \bf{\dag \ \ \ \ \ \ \ \ \ \ Using \ Equation \ \ \ \ \ \ \ \ \ \ \dag} \\ \\ \large{\underline{\boxed{\bf{(a + b)(a - b) = a^2 - b^2}}}}$

________________[Putting Values]

$\sf{\implies \dfrac{8 (\sqrt{5} + \sqrt{6})}{(\sqrt{5})^2 - (\sqrt{6})^2}} \\ \\ \sf{\implies \dfrac{8 (\sqrt{5} + \sqrt{6})}{5 - 6}} \\ \\ \sf{\implies \dfrac{8 (\sqrt{5} + \sqrt{6})}{-1}} \\ \\ \sf{\implies 8 (\sqrt{5} + \sqrt{6})} \\ \\ \large{\underline{\boxed{\bf{ 8 (\sqrt{5} + \sqrt{6})}}}}$

Answer 2

Answer:

The answer is 8√6 - 8√5.

Step-by-step explanation:

To solve : $\frac{8}{\sqrt{5} - \sqrt{6} }$

Concept : In order to rationalize  √a - √b in denominator, we multiply the numerator and denominator with √a + √b.

Formulas used : a² - b² = (a-b)(a+b)

Solution:

Step 1 : We multiply the numerator and denominator with √5 + √6.

$\frac{8}{\sqrt{5} - \sqrt{6} }$

Multiplying the numerator and denominator with √5 + √6

$\frac{8(\sqrt{5} + \sqrt{6} )}{(\sqrt{5} - \sqrt{6})(\sqrt{5} + \sqrt{6} ) }$.

Step 2 : Solve the denominator

$\frac{8(\sqrt{5} + \sqrt{6} )}{(\sqrt{5} - \sqrt{6})(\sqrt{5} + \sqrt{6} ) }$

= $\frac{8(\sqrt{5} + \sqrt{6} )}{(\sqrt{5}) ^{2} - (\sqrt{6}) ^{2} }$

= $\frac{8(\sqrt{5}+\sqrt{6}) }{5-6}$

= $\frac{8(\sqrt{5}+\sqrt{6}) }{-1}$

= - 8(√5 - √6)

Step 3 : Simplify

- 8(√5 - √6)

= -8√5 + 8√6

= 8√6 - 8√5

So, the answer is 8√6 - 8√5.

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