Question 345955: Write in simplified radical form by rationalizing the denominator.
root 3-2 over -5 root 3+8 Answer by jsmallt9(3758) (Show Source): 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.
To rationalize a binomial (two-term) denominator with square roots, we will take advantage of the pattern: . 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 and "b" being 8. So we need to multiply by the corresponding a-b: . And since we are multiplying the denominator by this, we must also multiply the numerator:
When we multiply this out, the denominator is easy because we know from the pattern how it works out: } or, in this case: . In the numerator we will just use FOIL (or whatever method you have learned to multiply binomials).
And we have a simplified fraction with a rational denominator.