Question

Rationalize \frac{6}{\sqrt 3}

Answer 1

\[\large \frac{6}{\sqrt3}\]To rationalize this, we'll attempt to get the irrational term out of the denominator.


To achieve this, we'll multiply our fraction by something that is EQUIVALENT to 1. When we multiply by 1, it doesn't change it VALUE of the fraction, it just changes how it looks.

If you take a number and divide it by itself, that is equivalent to 1. No matter how ugly it may look, as long as it's the same on the top and bottom, it's equivalent to one.

So we'll multiply our fraction by this term, \(\huge \frac{\sqrt3}{\sqrt3}\)

Answer 2

\[\large \frac{6}{\sqrt3}\cdot \frac{\sqrt3}{\sqrt3}\]Just multiply across, giving us,\[\large \frac{6 \sqrt3}{3}\]Understand how the bottom multiplied out?
We can do a little bit of simplification from here.

Answer 3

Since \(\large 6=3\cdot2\) , we can write our fraction as,

\[\large \frac{3\cdot2 \sqrt3}{3}\]
And from here you might notice that there is a 3 in the top AND the bottom. We can cancel those out.
\[\large \frac{\color{red}{\cancel{\color{black}{3}}}\cdot2 \sqrt3}{\color{red}{\cancel{\color{black}{3}}}}\]

Answer 4

Giving us a final answer of,\[\large 2 \sqrt 3\]