How do you simplify the expression 4 over square root of 7 + the square root of 3?

1 Answer
Sep 15, 2015

Answer:

# (sqrt(7) - sqrt(3))#

Explanation:

#4/(sqrt(7)+sqrt(3))#
#color(white)("XXXXX")#rationalizing the denominator:
#=4/(sqrt(7)-sqrt(3))xx(sqrt(7)+sqrt(3))/(sqrt(7)+sqrt(3))#

#=(4(sqrt(7)+sqrt(3)))/((sqrt(7))^2-(sqrt(3))^2)#

#=(4(sqrt(7)+sqrt(3)))/(7-3)#

#=(cancel(4)(sqrt(7)+sqrt(3)))/cancel(4)#