SOLUTION: How would I do this problem? Express 5 over 3-√2 with a rational denominator, in simplest radical form.

Question 275432: How would I do this problem? Express 5 over 3-√2 with a rational denominator, in simplest radical form.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Your denominator has two terms. To rationalize a denominator of two terms we take advantage of the pattern: . Every two-term expression (aka binomial) will match one of the two factors on the left side of the pattern. In your case, because you have a "-" between the two terms of your denominator, your denominator matches the (a-b) factor in the pattern. If we multiply your denominator by we will get, as we can see from the pattern, two perfect squares (with a "-" between them). This is exactly what you need to rationalize the denominator.

Of course we cannot multiply just the denominator by . We must also multiply the numerator by the same thing. Otherwise we are changing the value of the expression:

On top we use the Distributive Property. On the bottom, the pattern tells us what we will get:

which simplifies as follows:

and the denominator is now rational.
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SOLUTION: How would I do this problem? Express 5 over 3-&#8730;2 with a rational denominator, in simplest radical form.

SOLUTION: How would I do this problem? Express 5 over 3-√2 with a rational denominator, in simplest radical form.