Question

Create your own binomial expression with a radical in the second term.

Part 1: Identify its conjugate and explain, in complete sentences, why it is the conjugate.

Part 2: Multiply your original binomial expression and its conjugate. What happened to the radicals and why?

Answer 1

The pupose of a conjugate is to eliminate radicals, imaginary numbers, etc., so that the expression is real-valued.

So, for example, take a binomial expression like \[2-\sqrt{5}\].
The conjugate would then be \[2+\sqrt{5}.\]
Multiplying the two conjugates together gives the following expession:
\[(2-\sqrt{5})(2+\sqrt{5})=4+2\sqrt{5}-2\sqrt{5}-(\sqrt{5)^{2}}=4-5=-1\]
I hope that helps.