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

3 Answers
May 1, 2018

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

= (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

=(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.