Solving Equations with One Radical Term
Example
Solve for y:
Solution 

= 1 
Step 1 Isolate the radical term.
Subtract 4y from both sides. 

= 4y  1 
Step 2 Apply the Principle of Powers.
Square both sides. 

= (4y  1)^{2} 
Step 3 Solve the resulting equation.
Write the right side as a product.
FOIL the right side.
Subtract 16y^{2} from both sides.
Subtract 1 from both sides.

16y^{2} + 3
16y^{2} + 3
3
2 
= (4y  1)(4y  1)
= 16y^{2} + 8y + 1
= 8y + 1
= 8y 
Divide both sides by 8 and reduce. 

= y 
Step 4 Check the solution. 


The result
is an extraneous solution.
So, the equation
has no solution.
