What is the simplest form of the radical expression?
√2+√5/√2−√5
To simplify the given expression, we can rationalize the denominator. We do this by multiplying both the numerator and denominator by the conjugate of the denominator: √2 + √5.
√2 + √5 / √2 - √5
= (√2 + √5)(√2 + √5) / (√2 - √5)(√2 + √5)
= (√2 + √5)(√2 + √5) / (√2)^2 - (√5)^2
= (√2 + √5)(√2 + √5) / 2 - 5
= (√2)(√2) + (√2)(√5) + (√5)(√2) + (√5)(√5) / -3
= 2 + √10 + √10 + 5 / -3
= 7 + 2√10 / -3
= -(7 + 2√10) / 3
Thus, the simplest form of the radical expression √2 + √5 / √2 - √5 is -(7 + 2√10) / 3.