Question

Find the square root of :

$17+12\sqrt{2}$

• A. $\sqrt{2}+3$
• B. $\sqrt{4}+3$
• C. $\sqrt{8}+3$
• D. $\sqrt{8}+2$

Answer 1

The correct option is C $\sqrt{8}+3$

$17+12\sqrt{2}$

$=8+9+4\cdot 3\cdot \sqrt{2}$

$=8+9+2\cdot \sqrt{4}\cdot 3\cdot \sqrt{2}$

$=(\sqrt{8}{)}^2+(\sqrt{9}{)}^2+2\sqrt{8}\times \sqrt{9}$

$=(\sqrt{9}+\sqrt{8}{)}^2$

$=(3+\sqrt{8}{)}^2$...............Using $(a+b{)}^2=a^2+b^2+2ab$

$\therefore 17+12\sqrt{2}=(3+\sqrt{8}{)}^2$

So, the square root of $(17+12\sqrt{2})$ is $(3+\sqrt{8})$