Question

Convert the given surds $(2+\sqrt{3})(2-\sqrt{3})$ into its simplest form.

• A. $\sqrt{3}$
• B. $1$
• C. $4$
• D. $2\sqrt{3}$

Answer 1

Answer: (B)

$1$

Using distributive property $a(b+c)=a.b+a.c$, we have
$(2+\sqrt{3})(2-\sqrt{3})$
$=2(2-\sqrt{3})+\sqrt{3}(2-\sqrt{3})=2.2-2.\sqrt{3}+\sqrt{3}.2-\sqrt{3}.\sqrt{3}=4-2\sqrt{3}+2\sqrt{3}-3=4-3=1$
Hence, option $B$ is correct.