How do you rationalize x/(sqrt5-sqrt2)?

1 Answer
George C.
May 21, 2015

You can rationalize the denominator of this expression, by multiplying the numerator (top) and denominator (bottom) by the conjugate of sqrt(5)-sqrt(2), namely sqrt(5)+sqrt(2).

x/(sqrt(5)-sqrt(2))

= ((sqrt(5)+sqrt(2))x)/((sqrt(5)+sqrt(2))(sqrt(5)-sqrt(2)))

= ((sqrt(5)+sqrt(2))x)/(sqrt(5)sqrt(5)-sqrt(2)sqrt(2))

= ((sqrt(5)+sqrt(2))x)/(5-2)

= ((sqrt(5)+sqrt(2))x)/3

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