SOLUTION: what is the simplified expression of 3 + the square root of 7 divided by 2 minus the square root of 10

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Question 398060: what is the simplified expression of 3 + the square root of 7 divided by 2 minus the square root of 10
Answer by lwsshak3(11628) About Me  (Show Source):
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what is the simplified expression of 3 + the square root of 7 divided by 2 minus the square root of 10


The general rule is that you don't want to leave a radical in the denominator. This is called rationalizing the denominator.
To rationalize the given expression, multiply numerator and denominator by the conjugate off the denominator, then simplify.
(3+sqrt(7))/(2-sqrt(10))*2+sqrt(10)/(2+sqrt(10)
(3+sqrt(7))(2+sqrt(10))/(2-sqrt(10))(2+sqrt(10))
6+3sqrt(10)+2sqrt(7)+sqrt(70)/4-10 (difference of squares)
ans:6+3sqrt(10)+2sqrt(7)+sqrt(70)/-6