Solve Equation Including Cube Root

Example about solving equations with cube root .

Example 1


If $\dfrac{2}{\sqrt[3]{|x|+2}}=1$, then $|x|=$?

  1. $6$

  2. $7$

  3. $8$

  4. $9$

  5. $10$ and $1$

Solution


  1. Rewrite the given equation as follows $\dfrac{2}{\sqrt[3]{|x|+2}}=\dfrac{1}{1}$ and cross multiply to obtain

    $2 = \sqrt[3]{|x|+2}$

  2. Because of the cube root we rais both sides to the power 3

    $(2)^3 = (\sqrt[3]{|x|+2})^3$

  3. Use the rule $(\sqrt[3]x)^3=x$ to simplify the right side

    $8 = |x|+2$

  4. Solve for |x|.

    $|x|=6$

    Answer A