# How do you simplify sqrt67/sqrt7?

##### 2 Answers
Mar 22, 2015

When we simplify this problem, we are rationalizing the denominator.

For info on how to do this, check this site out: http://www.purplemath.com/modules/radicals5.htm

Now, let's solve this problem:

First thing, we multiply the expression by $\frac{\sqrt{7}}{\sqrt{7}}$. We can do this because $\frac{\sqrt{7}}{\sqrt{7}}$ is simply 1, and multiplying something by 1 doesn't change the nature of the expression.

So, our expression is this: $\frac{\sqrt{67}}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

Multiplying, we get: $\frac{\sqrt{469}}{\sqrt{49}}$

Since $\sqrt{49}$ simplifies to 7, we get: $\frac{\sqrt{469}}{7}$

Since, $\sqrt{469}$ is not something we can simplify, our final answer is: $\frac{\sqrt{469}}{7}$

Mar 22, 2015

In a calculator, the answer is $3.09377254682$

If by simply, you mean to rationalize the denominator, multiple both the numerator and the denominator by $\sqrt{7}$:

$\left(\frac{\sqrt{67}}{\sqrt{7}}\right) = \left(\frac{\sqrt{67} \cdot \sqrt{7}}{7}\right) = \frac{\sqrt{469}}{7}$