Question

simplify 3 + root 3 into 2 + root 2 whole square

Answer 1

Dear Student

$$\begin{gathered} Ifyourquestionis-{\left[(3+\sqrt{3})(2+\sqrt{2})\right]}^2 \\ thenansweris- \\ =(3+\sqrt{3}{)}^2(2+\sqrt{2}{)}^2 \\ =\left(9+6\sqrt{3}+3\right)\left(4+4\sqrt{2}+2\right)\left[\because {\left(a+b\right)}^2=a^2+2ab+b^2\right] \\ =\left(12+6\sqrt{3}\right)\left(6+4\sqrt{2}\right)=6\left(2+\sqrt{3}\right)\times 2\left(3+2\sqrt{2}\right) \\ =12\left(2+\sqrt{3}\right)\left(3+2\sqrt{2}\right)=12\left(6+4\sqrt{2}+3\sqrt{3}+2\sqrt{6}\right) \end{gathered}$$
$=72+48\sqrt{2}+36\sqrt{3}+24\sqrt{6}$
Regards