How do you simplify #2div (2+sqrt(2))#?

1 Answer
May 6, 2018

Answer:

#2-sqrt2#

Explanation:

#"to simplify a fraction with a radical on the denominator"#

#"multiply the numerator/denominator by the "color(blue)"conjugate"#
#"of the denominator"#

#"the conjugate of "a+-b" is "acolor(red)(∓)b#

#"the conjugate of "2+sqrt2" is "2color(red)(-)sqrt2#

#rArr2/(2+sqrt2)xx(2-sqrt2)/(2-sqrt2)#

#=(2(2-sqrt2))/((2+sqrt2)(2-sqrt2))#

#=(4-2sqrt2)/(4-2)=(4-2sqrt2)/2=2-sqrt2#