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

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Answer 1 · 2016-05-06T21:50:22

So we want to "rationalize" the denominator by removing the $sqrt3$ 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, $sqrt3 * sqrt3 = 3$

So, we can multiply both the top and the bottom by $sqrt3 / sqrt3$ to make the bottom into 3!!

$1/sqrt3 * (sqrt3 / sqrt3)$

Since $sqrt3 / sqrt3 = 0$ we haven't changed the value of anything, so this is good.

We finally have $sqrt3 / 3$

How do you rationalize the denominator and simplify 1/sqrt31/sqrt3?