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Rationalize: `1/(sqrt x + sqrt y)`

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spock2 | Student, Undergraduate | (Level 2) Honors

Posted May 28, 2012 at 3:35 AM via web

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Rationalize: `1/(sqrt x + sqrt y)`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 28, 2012 at 4:25 AM (Answer #1)

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The expression `1/(sqrt x + sqrt y)` has to be rationalized.

`1/(sqrt x + sqrt y)`

=> `(sqrt x - sqrt y)/((sqrt x + sqrt y)(sqrt x - sqrt y))`

=> `(sqrt x - sqrt y)/((sqrt x)^2 - (sqrt y)^2)`

=> `(sqrt x - sqrt y)/(x - y)`

The rationalized form of `1/(sqrt x + sqrt y) = (sqrt x - sqrt y)/(x - y)`

=> (sqrt x - sqrt y)/((sqrt x + sqrt y)(sqrt x - sqrt y))

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