Express `(7+sqrt5)/(3+sqrt5)` in the form of `m+n*sqrt 5` , where m and n are integers.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The expression `(7 + sqrt 5)/(3 + sqrt 5)` has to be expressed as `n + n*sqrt 5`

`(7 + sqrt 5)/(3 + sqrt 5)`

multiply the numerator and denominator by `3 - sqrt 5`

=> `((7 + sqrt 5)(3 - sqrt 5))/((3 + sqrt 5)(3 - sqrt 5))`

=> `((7 + sqrt 5)(3 - sqrt 5))/(9 - 5)`

=> `(21 + 3*sqrt 5 - 7*sqrt 5 - 5)/(9 - 5)`

=> `(16 - 4*sqrt 5)/4`

=> `4 - sqrt 5`

The expression is equivalent to `4 - sqrt 5`

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