How do you rationalize the denominator and simplify #(2+sqrt2)/sqrt3#?

1 Answer
Aug 2, 2017

Answer:

#(2sqrt3+sqrt6)/3#

Explanation:

#"to rationalise the denominator"#

#"multiply the numerator/denominator by " sqrt3#

#•color(white)(x)sqrtaxxsqrta=a#

#•color(white)(x)sqrtaxxsqrtb=sqrt(axxb)#

#rArr(2+sqrt2)/sqrt3xxsqrt3/sqrt3#

#=(sqrt3(2+sqrt2))/3larrcolor(red)" rational denominator"#

#=(2sqrt3+sqrt6)/3#