How do you rationalize the denominator and simplify $\frac{1}{\sqrt{3}}$ $1/sqrt3$ ?

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Answer 1 · 2016-05-06T21:50:22

So we want to "rationalize" the denominator by removing the $\sqrt{3}$ $sqrt3$ from the denominator, and replace it with a whole number.

Well, how can we manipulate the radical into a whole number?

Maybe we can multiply both the top and the bottom by the same number, and rationalize the bottom by doing so?

If you recall, $\sqrt{3} \cdot \sqrt{3} = 3$ $sqrt3 * sqrt3 = 3$

So, we can multiply both the top and the bottom by $\frac{\sqrt{3}}{\sqrt{3}}$ $sqrt3 / sqrt3$ to make the bottom into 3!!

$\frac{1}{\sqrt{3}} \cdot (\frac{\sqrt{3}}{\sqrt{3}})$ $1/sqrt3 * (sqrt3 / sqrt3)$

Since $\frac{\sqrt{3}}{\sqrt{3}} = 0$ $sqrt3 / sqrt3 = 0$ we haven't changed the value of anything, so this is good.

We finally have $\frac{\sqrt{3}}{3}$ $sqrt3 / 3$

How do you rationalize the denominator and simplify 1√31/sqrt3?