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a conjugate of a number means just flip the signs!

A conjugate of an binomial is a binomial (of course) that has its second term negated. Sorry if I explained it a little weird, but please bear with me. Let's say that you have a binomial $2-\sqrt{5}$ . The conjugate of that would be $2+\sqrt{5}$ . This topic is important because if you multiply these: $(2-\sqrt{5})(2-\sqrt{5})$ , you would get a difference of two squares, and which also results in a real number. (in this example, $4-5$ , or $(2)^2-2\sqrt{5}+2\sqrt{5}-(\sqrt{5})^2$ )

For this problem, the conjugate of $4+\sqrt{3}$ is $4-\sqrt{3}$ , because the second term is negated. Multiplying both out gives you $(4)^2-4\sqrt{3}+4\sqrt{3}-(\sqrt{3})^2$ or 16-3 or 13.

I hope you enjoyed this rather simple problem, enjoy Brilliant.org, explore the depths of it, and help the Brilliant community!

Conjugate of $a+\sqrt {b}$ is $a-\sqrt {b}$ . Sub a=4, b=3 and you get the answer, $\boxed {4-\sqrt {3}}$