Equations with cube roots
This Grade 6 algebra skill from Yoshiwara Elementary Algebra teaches students to solve equations that contain cube roots. Students learn to isolate the cube root, then cube both sides of the equation to eliminate the radical and find the solution. Unlike square roots, cube roots apply to negative numbers as well.
Key Concepts
Property To solve an equation where the variable is under a cube root, first isolate the cube root. Then, undo the cube root by cubing both sides of the equation. We do not have to check for extraneous solutions when we cube both sides of an equation.
Examples To solve $\sqrt[3]{y} = 4$, we cube both sides: $(\sqrt[3]{y})^3 = 4^3$, which gives the solution $y = 64$.
Solve $2\sqrt[3]{x 1} = 6$. First, isolate the radical by dividing by 2 to get $\sqrt[3]{x 1} = 3$. Now, cube both sides: $(\sqrt[3]{x 1})^3 = 3^3$, so $x 1=27$, which gives $x=28$.
Common Questions
How do you solve an equation with a cube root?
Isolate the cube root on one side, then cube both sides to eliminate the radical. For example, if cube_root(x) = 3, then x = 3^3 = 27.
What makes cube root equations different from square root equations?
Cube roots can have negative values. For example, cube_root(-8) = -2, whereas square roots of negative numbers are not real.
How do you check your solution to a cube root equation?
Substitute the solution back into the original equation and verify that the cube root of your answer equals the value on the other side.
Can cube root equations have no solution?
Unlike square root equations, cube root equations always have exactly one real solution because every real number has exactly one real cube root.
Where are equations with cube roots taught?
Equations with cube roots are covered in the Yoshiwara Elementary Algebra textbook for Grade 6.