Solve Equations With Cube Root 3√x

Tutorial on how to solve equations containing cube roots. Detailed solutions to examples, explanations and exercises are included.

The idea behind solving equations containing cube roots is to raise to power 3 in order to clear the cube root using the property

( 3√x ) 3 = x.

Examples with Solutions

Example 1

Find all real solutions to the equation

3√x - x = 0

Solution to Example 1:

Example 2

Find all real solutions to the equation

3√( x 2 + 2 x + 8 ) = 2

Solution to Example 2:

Exercises


Solve the following equations
1.   3√x - 4 x = 0
2.   3√( x 2 + 2 x + 61 ) = 4

Solutions to above exercises
1.   x = 0 , x = 1 / 8 , x = - 1 / 8
2.   x = 1 , x = -3

References and Links

Solve Equations, Systems of Equations and Inequalities.