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

( sqrt(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.

Example 1 : Find all real solutions to the equation


sqrt ( x + 1) = 4


Solution to Example 1:

Example 2 : Find all real solutions to the equation


sqrt ( 3 x + 1) = x - 3

Solution to Example 2:

Exercises:(answers further down the page)

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 on how to Solve Equations, Systems of Equations and Inequalities.






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Updated: February 2015

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