How do you rationalize the denominator and simplify $7/(1+sqrt2)$ ?

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Answer 1 · 2016-03-30T16:24:07

$= -7 (1 - sqrt2)$

$7 / ( 1 + sqrt2)$

We rationalize , by multiplying the expression by conjugate of the denominator , $(1 + sqrt2) = color(blue)( 1 - sqrt2$

$= (7 * color(blue)( (1 - sqrt2))) / (( 1 + sqrt2) * color(blue)(( 1 - sqrt2))$

$= (7 * color(blue)( (1 )) + 7 * color(blue)((- sqrt2))) / (( 1 + sqrt2) * color(blue)(( 1 - sqrt2))$

$= ((7 - 7 sqrt2)) / (( 1 ^2 - (sqrt2)^2)$

$= ((7 - 7 sqrt2)) / (( 1 - 2 )$

$= (7 (1 - sqrt2)) / (-1 )$

$= -7 (1 - sqrt2)$

How do you rationalize the denominator and simplify 7/(1+sqrt2)7/(1+sqrt2)?