Question

Find the square root of:

$47+4\sqrt{33}$.

• A. $\sqrt{44}+\sqrt{3}$
• B. $\sqrt{42}+\sqrt{3}$
• C. $\sqrt{24}+\sqrt{3}$
• D. $\sqrt{44}+\sqrt{2}$

Answer 1

The correct option is A $\sqrt{44}+\sqrt{3}$

$47+4\sqrt{33}$
$=44+3+\sqrt{16\times 33}=(\sqrt{44}{)}^2+(\sqrt{3}{)}^2+2\sqrt{4\times 33}$
$=\left({\sqrt{44}}^2\right)+(\sqrt{3}{)}^2+2\sqrt{44\times 3}$
$\sqrt{47+4\sqrt{33}}=(\sqrt{44}+\sqrt{3}{)}^2$
$47+4\sqrt{33}=\sqrt{44}+\sqrt{3}$