Question

Determine an equivalent expression by rationalizing the denominator: (5√3)/(4-√6)

Answer 1

Explanation:

so when you want to rationalize the denominator when it's in the form
`(a-√(b))` you multiply by the conjugate which is
`(a+√(b))` which is where the sign is the opposite. This is because it's using the difference of squares to get rid of the square root. Because
`(a-b)(a+b) = a^2-b^2` this will remove the square root since it's going to become square and the ab - ab will cancel so there will be no square root

Multiply by conjugate

`(5\sqrt3)/(4-\sqrt6) * (4+\sqrt6)/(4+\sqrt6)\\`

Simplify:

`(20√(3) + 5√(6 * 3))/(16-6)`

Simplify radical

`(20√(3) + 15√(2))/(10)\\`

You could go further and do

`2√(3) + 1.5√(2)`