Question

Can someone help me with these two problems please.

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

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

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

Answer 1

So you just want to make up some irrational number. Say its:
\[3+\sqrt{2}\]
Its conjugate would be:
\[3-\sqrt{2}\]
When you multiply them (using the FOIL technique) you get:
\[(3+\sqrt{2})(3-\sqrt{2}) = (3)(3)-(3)(\sqrt{2})+(3)(\sqrt{2})-(\sqrt{2})(\sqrt{2})\]
Noitice that the two middle terms will cancel out, and the last term wont be irrational anymore (this always happens when multiplying an irrational number with its conjugate)