# How do you rationalize the denominator and simplify sqrt21/sqrt55?

Apr 9, 2015

The fraction does not change if both numerator and denominator are multiplied by the same number.
Multiply them by $\sqrt{55}$.
The result will be
$\frac{\sqrt{21} \cdot \sqrt{55}}{\sqrt{55} \cdot \sqrt{55}} = \frac{\sqrt{21} \cdot \sqrt{55}}{{\sqrt{55}}^{2}}$

The denominator is now equal to $55$ since the definition of $\sqrt{55}$ is a number, which produces $55$ if squared.

As for numerator, we can use the following property of square root for any two non-negative numbers:
$\sqrt{A} \cdot \sqrt{B} = \sqrt{A \cdot B}$
Using this property, we can represent the numerator as
$\sqrt{21} \cdot \sqrt{55} = \sqrt{21 \cdot 55} = \sqrt{1155}$

The final expression is
$\frac{\sqrt{1155}}{55}$