Question 248471
I'm assuming the problem is to solve {{{sqrt(x^2+8) = 3}}}<br>
To solve for a variable in a square root:<ol><li>Isolate the square root on sone side of the equation.</li><li>Square both sides</li><li>Solve the new equation.</li><li>Check your answers. This more than just a good idea. It is important because squaring both sides of an equation, like we did in step #2, can introduce what are called extraneous solutions. Extraneous solutions are solutions which work in the squared equation but do not work in the original equation.</li></ol>
1. Isolate the square root. Your square root is already by itself on the left side.<br>
2. Square both sides:
{{{(sqrt(x^2+8))^2 = (3)^2}}}
{{{x^2 + 8 = 9}}}<br>
3. Solve:
Subtract 9 from each side:
{{{x^2 - 1 = 0}}}
Factor:
{{{(x+1)(x-1) = 0}}}
x+1 = 0 or x=1 = 0
x = -1 or x = 1<br>
4. Check your answers. (Always use the original equation to check.)
Checking x = -1:
{{{sqrt((-1)^2+8) = 3}}}
{{{sqrt(1+8) = 3}}}
{{{sqrt(9) = 3}}}
{{{3 = 3}}}  Check!
Checking x = 1:
{{{sqrt((1)^2+8) = 3}}}
{{{sqrt(1+8) = 3}}}
{{{sqrt(9) = 3}}}
{{{3 = 3}}}  Check!<br>
(Note: Both answers checked out this time. But don't forrget this step. There will be times when one or more of your solutions are extraneous and muct be rejected.)