Question
What is the simplest form of the expression?
square root 3 - square root 6 over square root 3 + square root 6
square root 3 - square root 6 over square root 3 + square root 6
Answers
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Answered by
GPT 3.5
To simplify the expression:
(sqrt(3) - sqrt(6)) / (sqrt(3) + sqrt(6))
Rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator:
((sqrt(3) - sqrt(6)) * (sqrt(3) - sqrt(6))) / ((sqrt(3) + sqrt(6)) * (sqrt(3) - sqrt(6)))
= (3 - 2sqrt(18) + 6) / (3 - 6)
= (9 - 2sqrt(18)) / (-3)
= (-9 + 2sqrt(18)) / 3
= -3 + 2sqrt(2)
Therefore, the simplest form of the expression is -3 + 2sqrt(2).
(sqrt(3) - sqrt(6)) / (sqrt(3) + sqrt(6))
Rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator:
((sqrt(3) - sqrt(6)) * (sqrt(3) - sqrt(6))) / ((sqrt(3) + sqrt(6)) * (sqrt(3) - sqrt(6)))
= (3 - 2sqrt(18) + 6) / (3 - 6)
= (9 - 2sqrt(18)) / (-3)
= (-9 + 2sqrt(18)) / 3
= -3 + 2sqrt(2)
Therefore, the simplest form of the expression is -3 + 2sqrt(2).
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