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What is the simplest form of the radical expression?
√2+√5/√2−√5
To simplify the radical expression, we must rationalize the denominator.
First, we need to multiply the numerator and denominator by the conjugate of the denominator:
(√2+√5) * (√2+√5)/(√2-√5) * (√2+√5)
Using the difference of squares, we have:
(2 + 2√2√5 + 5)/(2 - 5)
Simplifying further, we get:
(7 + 2√10)/-3
Thus, the simplest form of the radical expression is:
-(7 + 2√10)/3