Question

State whether True or False

The square of $3+2\sqrt{5}$ is $29+12\sqrt{5}$

Answer 1

By using formula $(a+b{)}^2=a^2+2ab+b^2$, we get
$\therefore {(3+2\sqrt{5})}^2=(3{)}^2+2(3\left)\right(2\sqrt{5})+(2\sqrt{5}{)}^2$
$=9+12\sqrt{5}+20$
$=29+12\sqrt{5}$