Question

To simplify the radical below, which of the following expressions would be multiplied by the radical?

Answer 1

For this case, we must simplify the following expression:

`\frac {2 \sqrt {15}} {- 4- \sqrt {12}}`

We must rationalize the expression, the rationalization consists in eliminating the roots of the denominator, for it, we multiply the numerator and denominator by another expression equal to the initial denominator but with the sign changed to the root. That is, we must multiply the numerator and denominator by:
`{-4+ \sqrt {12}}`

Thus, we must multiply by:
`\frac {-4 + \sqrt {12}} {- 4+ \sqrt {12}}`

Answer:

Option A

Answer 2

-4 + sqrt(12)

-----------------

-4+ sqrt(12)

Choice A

Explanation:

when you have a radical expression in the denominator, you multiply by the conjugate to clear the radical in the denominator

if your expression in the denominator is

a+sqrt(b) you multiply by a- sqrt (b)

now remember what you do to the bottom, you do to the top

so you will have to multiply the numerator by the same thing

you will multiply by

a- sqrt(b)

------------

a- sqrt(b)

in this case we have -4 -sqrt(12)

a = -4

b = -sqrt(12)

so we will multiply by

-4 + sqrt(12)

-----------------

-4+ sqrt(12)