How do you rationalize the denominator and simplify $1/(5+sqrt7)$ ?

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Answer 1 · 2016-04-05T17:29:59

$= (5 - sqrt7) / 18$

$1 / ( 5 +sqrt7$

We rationalise the expression by multiplying it by the conjugate of the denominator. $color(blue)( ( 5 - sqrt7)$

$= (1 * color(blue)(( 5 - sqrt7))) / (( 5 +sqrt7) * color(blue)( ( 5 - sqrt7))$

$= (1 * color(blue)(( 5)) + 1 * color(blue)(( - sqrt7))) / (( 5 +sqrt7) * color(blue)( ( 5 - sqrt7))$

$= (5 - sqrt7) / (( 5 +sqrt7) * color(blue)( ( 5 - sqrt7))$

$= (5 - sqrt7) / (( 5 ^2 - (sqrt7)^2)$

$= (5 - sqrt7) / (25 - 7)$

$= (5 - sqrt7) / 18$

How do you rationalize the denominator and simplify 1/(5+sqrt7)1/(5+sqrt7)?