# How do you simplify (11y)/sqrt3?

Mar 12, 2018

$\frac{11 y \sqrt{3}}{3}$

#### Explanation:

The simplification required is to remove the root from the denominator of the fraction (so that roots are confined to the numerator).

This may be achieved by multiplying by $1$ (so that the value of the overall expression is unchanged), but choosing an appropriately constructed expression that evaluates to $1$ (noting that anything divided by itself (excluding zero) equals $1$).

The specially chosen instance of $1$ requires a number in its denominator that will remove the root. This can be achieved by multiplying by something divided by $\sqrt{3}$, as $\sqrt{3} \times \sqrt{3} = 3$. To ensure the complete number is $1$, the numerator must also have $\sqrt{3}$.

So, the required simplification is

$\frac{11 y}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$

$\frac{11 y \sqrt{3}}{3}$

Mar 12, 2018

$\frac{11 y}{\sqrt{3}} = \frac{11 y \sqrt{3}}{3}$

#### Explanation:

Simplify by rationalizing the denominator:

$\frac{11 y}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$

$= \frac{11 y \times \sqrt{3}}{\sqrt{3}} ^ 2$

$= \frac{11 y \sqrt{3}}{3}$