SOLUTION: when √(2z+1)+√(3z+4)= 7 the value of z is given by

Isolate one of the radical terms



We square both sides:



Squaring the square root on the left takes away the radical:
Write the right side twice multiplied by itself, so we can use FOIL:





Combine the radical terms on the right



Isolate the radical term on the left



Square both sides:







Factor the right side:



Use the zero factor property:

        z - 4 = 0;   z-480 = 0
            z = 4;       z = 480

We must always check radical equations with square
or even roots for extraneous solutions:

Checking z=4









So 4 is a solution.

Checking x=480







So 480 is an extraneous answer, not a solution.

The only solution is z = 4

Edwin