What is the simplest form of the radical expression? 2√+5√ / 2√−5√
sqrt(2) + sqrt(5) / sqrt(2) - sqrt(5)
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To simplify the radical expression:
(√2 + √5) / (√2 - √5)
First, we need to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator, which is (√2 + √5):
(√2 + √5) / (√2 - √5) * (√2 + √5) / (√2 + √5)
This gives us:
(√2 + √5)^2 / ((√2)^2 - (√5)^2)
Expanding the numerator:
(√2 + √5)(√2 + √5) = 2 + 2√10 + 5 = 7 + 2√10
Expanding the denominator:
((√2)^2 - (√5)^2) = 2 - 5 = -3
Now, our expression becomes:
(7 + 2√10) / -3
So, the simplest form of the given radical expression is:
(7 + 2√10) / -3