Question

Question #656ba

Answer 1

Please see below.

Explanation:

Hi Ana,

Multiplying by the conjugate is multiplying `(a+b)` by `(a-b)`. It is independent of whether each has a radical expression in it or not. It is typically done in solving rational functions where you multiply both the numerator and the denominator by the conjugate of one of them. For example:

`(a+b)/(a-b)=((a+b)(a-b))/((a-b)(a-b))=(a^2-b^2)/(a-b)^2`

It is done to make it easier to solve a given function because it makes it possible to simplify it.

Rationalizing a fraction that has a radical in the denominator could involve multiplying both top and bottom by the conjugate of the denominator if it looks something like:

`a/(sqrtb-sqrtc)`

You can do this:

`(a(sqrtb+sqrtc))/((sqrtb-sqrtc)(sqrtb+sqrtc))=(a(sqrtb+sqrtc))/(b-c)`

But if it looks like:

`a/(sqrt(b+c)`

You can rationalize it by multiplying by the denominator itself:

`(asqrt(b+c))/(sqrt(b+c)*sqrt(b+c))=(asqrt(b+c))/(b+c)`

We rationalized it without using any conjugates.