SOLUTION: how do you answer square root of 9 +4 over square root of 8 +6 I can't find the square root symbol on my keyboard,sorry! Thanks for your help!

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Question 242673: how do you answer
square root of 9 +4
over
square root of 8 +6
I can't find the square root symbol on my keyboard,sorry!
Thanks for your help!
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!

With a square root (which is irrational) in the denominator, the problem is to rationalize the denominator. But before we start we are going to simplify the square roots we do have.

Substituting for these two we get:

which simplifies to:

Now we can try to rationalize the denominator. With two terms, this denominator is a little harder to rationalize than if it was just one term. To rationalize two-term denominators we take advantage of the pattern: . All two-term expressions fit either the (a+b) or the (a-b) part of the pattern. And as we can see, the right side is a two-term expression of perfect squares! Expressions like (a+b) and (a-b) are called conjugates. So to rationalize a two-term denominator all we have to do is multiply the numerator and denominator by the conjugate of the denominator.

Our denominator is . Its conjugate is . So this is what we will use to multiply the numerator and denominator:

Multiplying we get:

which simplifies to:

And last of all, we reduce the fraction. Factor out 2 in the numerator:

Cancel the 2's:

or

or