Question

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

Answer 1

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`

Answer 2

`= (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`

Answer 3

`=(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.