Question

A = 5+2√6 so what is the value of √a -1/√a

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

$\rm a = 5+2\sqrt{6}$

$\bf\dashrightarrow \sqrt{a} =\sqrt{ 5+2\sqrt{6}}$

$\rm\dashrightarrow \dfrac{1}{\sqrt{a}} =\dfrac{1}{\sqrt{ 5+2\sqrt{6}}}$

Rationalising the denominator by its conjugate.

$\rm\dashrightarrow \dfrac{1}{\sqrt{a}} =\dfrac{1}{\sqrt{ 5+2\sqrt{6}}} \times \dfrac{\sqrt{5-2\sqrt{6}}}{\sqrt{5-2\sqrt{6}}}$

We know that,

$\rm\dashrightarrow \dfrac{1}{\sqrt{a}} = \dfrac{\sqrt{5-2\sqrt{6}}}{(\sqrt{ 5+2\sqrt{6}})(\sqrt{5-2\sqrt{6}})}$

$\rm\dashrightarrow \dfrac{1}{\sqrt{a}}= \dfrac{\sqrt{5-2\sqrt{6}}}{\sqrt{ (5+2\sqrt{6})(5-2\sqrt{6})}}$

(a + b)(a - b) = a² - b²

$\rm\dashrightarrow \dfrac{1}{\sqrt{a}}= \dfrac{\sqrt{5-2\sqrt{6}}}{\sqrt{ (5)^2-(2\sqrt{6})^2}}$

$\rm\dashrightarrow \dfrac{1}{\sqrt{a}}= \dfrac{\sqrt{5-2\sqrt{6}}}{\sqrt{ 25-24}}$

$\rm\dashrightarrow \dfrac{1}{\sqrt{a}}= \dfrac{\sqrt{5-2\sqrt{6}}}{\sqrt{1}}$

$\rm\dashrightarrow \dfrac{1}{\sqrt{a}}= \dfrac{\sqrt{5-2\sqrt{6}}}{1}$

$\bf\dashrightarrow \dfrac{1}{\sqrt{a}}= \sqrt{5-2\sqrt{6}}$

Hence,

$\rm\sqrt{a} - \dfrac{1}{\sqrt{a}} = \sqrt{ 5+2\sqrt{6}} -\sqrt{5-2\sqrt{6}} =\bf 2\sqrt{2}$