document.write( "Question 345955: Write in simplified radical form by rationalizing the denominator.
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\n" ); document.write( "root 3-2 over -5 root 3+8 \n" ); document.write( "

Algebra.Com's Answer #247414 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
I assume by \"root\" you mean square root. Please be specific in the future because there are also cube roots, 4th roots, 5th roots, etc.

\n" ); document.write( " $\"%28sqrt%283%29-2%29%2F%28-5sqrt%283%29%2B8%29\"$
\n" ); document.write( "To rationalize a binomial (two-term) denominator with square roots, we will take advantage of the pattern: $\"%28a%2Bb%29%28a-b%29+=+a%5E2+-+b%5E2\"$ . This shows us how to multiply a two term expression like a+b, a-b, or your denominator and turn it into an expression of perfect squares!. You denominator has a \"+\" between the two terms so it will play the role of a+b with \"a\" being $\"-5sqrt%283%29\"$ and \"b\" being 8. So we need to multiply by the corresponding a-b: $\"-5sqrt%283%29-8\"$ . And since we are multiplying the denominator by this, we must also multiply the numerator:
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\n" ); document.write( "When we multiply this out, the denominator is easy because we know from the pattern how it works out: $\"a%5E2+-+b%5E2\"$ } or, in this case: $\"%28-5sqrt%283%29%29%5E2+-+%288%29%5E2\"$ . In the numerator we will just use FOIL (or whatever method you have learned to multiply binomials).
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\n" ); document.write( " $\"%28-5%2A3+-8sqrt%283%29+%2B10sqrt%283%29+-16%29%2F%2825%2A3+-+64%29\"$
\n" ); document.write( " $\"%28-15++-8sqrt%283%29+%2B10sqrt%283%29+-16%29%2F%2875+-+64%29\"$
\n" ); document.write( " $\"%28-31+%2B2sqrt%283%29%29%2F11\"$
\n" ); document.write( "And we have a simplified fraction with a rational denominator. \n" ); document.write( "

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