Question

The value of $\frac{\sqrt{90}-\sqrt{10}}{\sqrt{10}}$ is _________.

Answer 1

Simplify the given expression:

$\begin{array}{rcl}\frac{\sqrt{90}-\sqrt{10}}{\sqrt{10}}& =& \frac{\sqrt{9\times 10}-\sqrt{10}}{\sqrt{10}}\end{array}$

$\begin{array}{rcl}& =& \frac{\sqrt{9}·\sqrt{10}-\sqrt{10}}{\sqrt{10}}\end{array}$ $[\because \sqrt{a·b}=\sqrt{a}·\sqrt{b}]$

$\begin{array}{rcl}& =& \frac{3\sqrt{10}-\sqrt{10}}{\sqrt{10}}\\ & =& \frac{\sqrt{10}\left(3-1\right)}{\sqrt{10}}\left[\mathrm{Take}\sqrt{10}\mathrm{common}\right]\\ & =& \frac{2\cancel{\sqrt{10}}}{\cancel{\sqrt{10}}}\\ & =& 2\end{array}$

Final Answer: Hence, the answer is $\mathbf{2}$.