1 9- 8 is equal to: - Vidyadip

MCQ

$\frac{1}{\sqrt9-\sqrt8}$ is equal to:

✓
$3+2\sqrt2$
B
$\frac{1}{3+2\sqrt2}$
C
$3-2\sqrt2$
D
$\frac{3}{2}-\sqrt2$

✓

Answer

Correct option: A.

$3+2\sqrt2$

$\frac{1}{\sqrt9-\sqrt8}$
$=\frac{1}{\sqrt9-\sqrt8}\times\frac{{\sqrt9+\sqrt8}}{{\sqrt9+\sqrt8}}$
$\frac{{\sqrt9+\sqrt8}}{\big(\sqrt9\big)^2-\big(\sqrt8\big)^2}$
$=\frac{{\sqrt9+\sqrt8}}{9-8}$
$={\sqrt9+\sqrt8}$
$=3+2\sqrt2$
Hence, correct option is $(a)$.

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