# How do you simplify sqrt(1) / sqrt (7) times sqrt(7) / sqrt(11)?

##### 1 Answer
Jun 19, 2016

$= \frac{\sqrt{11}}{11}$

#### Explanation:

$\left(\frac{\sqrt{1}}{\textcolor{b l u e}{\sqrt{7}}}\right) \cdot \left(\frac{\textcolor{b l u e}{\sqrt{7}}}{\sqrt{11}}\right)$

We can observe that color(blue)(sqrt7 is present in denominator of first term and numerator of second and hence can be cancelled.

$= \left(\frac{\sqrt{1}}{\cancel{\sqrt{7}}}\right) \cdot \left(\frac{\cancel{\sqrt{7}}}{\sqrt{11}}\right)$

$= \frac{\sqrt{1}}{\sqrt{11}}$

Now we rationalise the expression by multiplying the numerator and denominator of the expression by $\sqrt{11}$

=(sqrt1 * color(blue)(sqrt11))/(sqrt11 * color(blue)(sqrt11)

=(sqrt11)/(sqrt (11 *11)

=(sqrt11)/(sqrt (11 ^2)

$= \frac{\sqrt{11}}{11}$