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

Answer 1

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#

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Answer 2

Eva Adamson

To rationalize the denominator and simplify 1/sqrt(3), you multiply both the numerator and denominator by sqrt(3). This results in (1 * sqrt(3))/(sqrt(3) * sqrt(3)), which simplifies to sqrt(3)/3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.