# What is 7 over the square root of 27?

Jul 24, 2015

$\frac{7 \sqrt{3}}{9}$

#### Explanation:

Start by writing your expression, which features $7$ in the numerator and $\sqrt{27}$ in the denominator.

7/(sqrt(27)

Now, the important thing to realize here is that you can write $27$ as

27 = 9 * 3 = 3 * 3 * 3 = 3""^2 * 3

This means that the denominator becomes

$\sqrt{27} = \sqrt{3 {\text{^2 * 3) = sqrt(3}}^{2}} \cdot \sqrt{3} = 3 \sqrt{3}$

The expression is now

$\frac{7}{3 \cdot \sqrt{3}}$

Next, you have to rationalize the denominator, which you can do by multiplying the numerator and the denominator by $\sqrt{3}$, to get

(7 * sqrt(3))/(3 * underbrace(sqrt(3) * sqrt(3))_(color(blue)("=3))) = (7 * sqrt(3))/(3 * color(blue)(3)) = color(green)((7 sqrt(3))/9)