How do you rationalize the denominator and simplify 5/(sqrt3-1)?

1 Answer
MathFact-orials.blogspot.com
Jul 5, 2016

(5sqrt3+5)/2=(5/2)(sqrt3+1)

Explanation:

We can simplify this fraction by using a clever use of the number 1 and also by keeping in mind that something in the form of:

(a+b)(a-b)=a^2-b^2, so that will allow us to rationalize the denominator without getting into messy square root issues.

Starting with the original:

5/(sqrt3-1)

We can now multiply by 1 and not change the value of the fraction:

5/(sqrt3-1)(1)

and we can now pick a value of 1 that will suit our purposes. We have something in the form of (a-b) already in the denominator, so let's multiply by (a+b):

5/(sqrt3-1)((sqrt3+1)/(sqrt3+1))

which gets us:

(5(sqrt3+1))/((sqrt3-1)(sqrt3+1))

simplifying:

(5sqrt3+5)/(3-1)=(5sqrt3+5)/2=(5/2)(sqrt3+1)

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