Solve Equations With Square Root (√)

Tutorial on how to solve equations containing square roots. Detailed solutions to examples, explanations and exercises are included.
The main idea behind solving equations containing square roots is to raise to power 2 in order to clear the square root using the property

( √x ) 2 = x.
The above holds only for x greater than or equal to 0. In solving equations we square both sides of the equations and instead of putting similar conditions we check the solutions obtained.

Examples with Solutions

Example 1

Find all real solutions to the equation
√( x + 1) = 4

Solution to Example 1:

Example 2

Find all real solutions to the equation
√( 3 x + 1) = x - 3

Solution to Example 2:

Exercises

Solve the following equations
1.   sqrt(2 x + 15) = 5
2.   sqrt(4 x - 3) = x - 2

Solutions to above exercises

1.   x = 5
2.   x = 7

More References and Links

Solve an Equation with a Radical.
Solve an Equation With Two Radicals.
Solve Equations, Systems of Equations and Inequalities.