SOLUTION: 2 square root of 5 ----------- --------- -4 + square root of 8

Question 138234This question is from textbook Glencoe Mathmatics (Algebra 1)
: 2 square root of 5
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-4 + square root of 8 This question is from textbook Glencoe Mathmatics (Algebra 1)

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Simplifying this expression involves a process called rationalizing the denominator. The process results in a rational number in the denominator and whatever happens to the numerator as a result, happens.

You can't simply square the denominator because you would still end up with a term containing a radical, so you need another technique. It involves using the 'difference of two squares' factorization in reverse. Specifically, if you multiply the denominator by its conjugate (the conjugate of is )

The conjugate of your denominator is .

Now we use the multiplicative identity rule, namely . But we need to multiply your fraction by 1 in the form of .

Here's the whole thing:

.

Now all you need to do is multiply the two fractions in the normal way and simplify the result. Let me know if you are still having difficulty with that part.

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