# What is the conjugate when dealing with radical expressions?

##### 1 Answer

Here's an example.

Let

We will be left with the following:

The conjugate has as goal to make a difference of squares, which is why we use it to rationalize denominators. We can find the conjugate by switching the middle sign in the binomial expression.

Hence, the conjugate of

Let's try multiplying the two expressions to see what happens.

So, we start with an expression with lots of irrational numbers, and we multiply it by it's conjugate and get a rational number! Math is so cool sometimes!

Here are a few exercises for your practice. Send me a note when you're ready to be given the answers.

**Practice exercises:**

•Write the conjugate

•Multiply the expression by its conjugate

•Simplify the expression if necessary

a)

b)

c)

d)

Hopefully this helps, and good luck!