Question
$\frac{1}{\sqrt9-\sqrt8}$ is equal to:
✓
Answer
- $3+2\sqrt2$
Solution:
$\frac{1}{\sqrt9-\sqrt8}$
$=\frac{1}{\sqrt9-\sqrt8}\times\frac{{\sqrt9+\sqrt8}}{{\sqrt9+\sqrt8}}$
$\frac{{\sqrt9+\sqrt8}}{\big(\sqrt9\big)^2-\big(\sqrt8\big)^2}$
$=\frac{{\sqrt9+\sqrt8}}{9-8}$
$={\sqrt9+\sqrt8}$
$=3+2\sqrt2$
Hence, correct option is (a).
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The following observations have been arranged in ascending order: 18, 20, 25, 26, 30, x, 37, 38, 39, 48. If the median of the data is 35, then the value of x is:
Write the correct answer in the following:
The number of dimension, a point has:
The number of dimension, a point has:
The base of a Pyramid is:
Which of the following is irrational?
The zeros of the polynomial $p(x) = 3x^2 - 1$ are:
→→
Write the correct answer in the following: If $x + 1$ is a factor of the polynomial $2x^2 + kx,$ then the value of $k$ is.
→The mid-value of a class interval is 42. If the class size is 10, then the upper and lower limits of the class are:
In the adjoining figure, $\text{AB}\bot\text{BE}$ and $\text{FE}\bot\text{BE}.$ If $AB = FE$ and $BC = DE,$ then.
→The value of $(243)^{\frac{1}{5}}$ is:
→