Question

If $\sqrt{\frac{{(4+\sqrt{x+3})}^2}{6}+3}=3$, then $x$ is equal to:

• A. $22$
• B. $6$
• C. $3$
• D. $1$

Answer 1

The correct option is D $1$

Given,

$\sqrt{\frac{{(4+\sqrt{x+3})}^2}{6}+3}=3$.

$⟹$ $\frac{{(4+\sqrt{x+3})}^2}{6}+3=9$
$⟹$ $\frac{{(4+\sqrt{x+3})}^2}{6}=6$
$⟹$ $(4+\sqrt{x+3}{)}^2=36$
$⟹$ $4+\sqrt{x+3}=6$
$⟹$ $\sqrt{x+3}=2$
$⟹$ $x+3=4$
$⟹$ $x=4-3$

$⟹$ $x=1$.

Therefore, option $D$ is correct.