How do you simplify #2div( 5 - sqrt3)#?

3 Answers
May 1, 2018

Answer:

Multiply denominator and numerator with #5+sqrt3#

Explanation:

Remember that (a+b)(a-b) =#a^2-b^2#
That gives you
#2/(5-sqrt3)#
=#[2(5+sqrt3)]/[(5+sqrt3)(5-sqrt3)]#
= #[2(5+sqrt3)]/(25-9)#
= #(5+sqrt3)/8#

May 1, 2018

Answer:

# = (5 + sqrt(3))/11#

Explanation:

#= 2/(5-sqrt(3)#
We multiply and divide the fraction by the denominator's conjugate to eliminate the irrationality in the denominator.

#= 2/(5-sqrt(3))xx (5+sqrt(3))/(5+ sqrt(3))#
Using #(a - b)(a+b) = a^2 - b^2#, we have
# = (2(5+sqrt(3)))/22#
# = (5 + sqrt(3))/11#

May 1, 2018

Answer:

#=(5+sqrt3)/11#

Explanation:

To rationalize this expression, multiply both sides by the bottom's inverse #(5+sqrt3)#
#2/(5-sqrt3)*(5+sqrt3)/(5+sqrt3)# Distribute:
#=(10+2sqrt3)/(25+5sqrt3-5sqrt3-3)# Combine like terms:
#=(10+2sqrt3)/22# Divide by #2#:
#=(5+sqrt3)/11# Simplest form.