Question

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Answer 1

Answer:

$\frac{1}{\sqrt9-\sqrt8}\;=\;3+2\sqrt2$

Step-by-step explanation:

Given :

$\frac{1}{\sqrt9-\sqrt8}$

To find :

To prove that $\frac{1}{\sqrt9-\sqrt8}$ is equal to $3+2\sqrt2$.

Solution :

$\frac{1}{\sqrt9-\sqrt8}\;*\;\frac{\sqrt9+\sqrt8}{\sqrt9+\sqrt8}$

$(a+b)(a-b)=a^2-b^2$

$\frac{\sqrt9+\sqrt8}{(\sqrt9)^2-(\sqrt8)^2}$

$\frac{\sqrt9+\sqrt8}{9-8}$

$\frac{3+2\sqrt2}{1}$

$3+2\sqrt2$

Hence, proved !

Answer 2

$\tt\huge\purple{hello!!!}$

HERE IS UR ANSWER

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$\frac{1}{ \sqrt{9} - \sqrt{8} } \\ rationalising \: denominator \\ \frac{1}{ \sqrt{9} - \sqrt{8} } \times \frac{ \sqrt{9} + \sqrt{8} }{ \sqrt{9} + \sqrt{8} } \\ \frac{ \sqrt{9} + \sqrt{8} }{9 - 8} \\ \sqrt{9} + \sqrt{8} \\ 3 + 2 \sqrt{2}$