#sqrt (t) = sqrt (t - 12) + 2? #solve the radical equations, of possible.
THIS ANSWER IS INCORRECT. SEE THE CORRECT SOLUTION ABOVE.
Start by squaring both sides to get rid of one of the radicals, then simplify and combine like terms.
Then operate on both sides of the equation to isolate the other radical.
And square both sides again to get rid of the other radical.
When working with radicals, always check your solutions to make sure they aren't extraneous (make sure they don't cause there to be a square root of a negative number). In this case both
Rearrange the equation:
#sqrt(t) - 2 = sqrt(t - 12)#
Square both sides:
#(sqrt(t) - 2)^2 = (sqrt(t - 12))^2#
#t - 4sqrt(t) + 4 = t - 12#
#16 = 4sqrt(t)#
#4 = sqrt(t)#
Square both sides once more.
#16 = t#
Check the solution is accurate.
#sqrt(16) = sqrt(16 - 12) + 2 -> 4 = 4 color(green)(√)#
Hopefully this helps!