How do you solve sqrt(x-5) = 2sqrt6?

May 25, 2016

$x = 29$

Explanation:

Square both sides.

${\left(\sqrt{x - 5}\right)}^{2} = {\left(2 \sqrt{6}\right)}^{2}$

On the left side, the square root and the exponent of $2$ undo one another, leaving just $x - 5$.

On the right side, to square $2 \sqrt{6}$, we see that ${\left(2 \sqrt{6}\right)}^{2} = {2}^{2} \cdot {\left(\sqrt{6}\right)}^{2} = 4 \cdot 6 = 24$.

$x - 5 = 24$

$x = 29$

May 25, 2016

$x = 29$
$x - 5 = {\left(2 \sqrt{6}\right)}^{2} \to x - 5 = {2}^{2} \times 6 \to x - 5 = 24$
$x = 29$