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

1 Answer
Mar 30, 2016

Answer:

#= -7 (1 - sqrt2)#

Explanation:

#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)) #

  • Applying property:
    #color(blue)((a + b ) (a-b) = a^2 - b^2# to the denominator.

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

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

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

#= -7 (1 - sqrt2)#