# How do you solve sqrt(x+9)=sqrt3+sqrtx and check your solution?

Oct 15, 2016

$x = 3$

#### Explanation:

square both sides:

${\left(\sqrt{x + 9}\right)}^{2} = {\left(\sqrt{3} + \sqrt{x}\right)}^{2}$

$x + 9 = 3 + x + 2 \sqrt{3 x}$

$6 = 2 \sqrt{3 x}$

Square again to get rid of the square root on the right.

${6}^{2} = {\left(2 \sqrt{3 x}\right)}^{2}$

$36 = 4 \left(3 x\right)$

$36 = 12 x$

$x = 3$

Finally, don't forget to check your solution in the original equation.

sqrt(9 + 3) =^? sqrt(3) + sqrt(3)

sqrt(12) =^? 2sqrt(3)

sqrt(4 xx 3) =^? 2sqrt(3)

$2 \sqrt{3} = 2 \sqrt{3}$

Hopefully this helps!