Solve for x cube root of x^2-8=2

$\sqrt[3]{x^{2}} - 8 = 2$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x^{2}}$ as $x^{\frac{2}{3}}$ .

$x^{\frac{2}{3}} - 8 = 2$

Step 2

Move all terms not containing $x$ to the right side of the equation.

Add $8$ to both sides of the equation.

$x^{\frac{2}{3}} - 2 = 8$

Add $2$ to both sides of the equation.

$x^{\frac{2}{3}} = 8 + 2$

Add $8$ and $2$ .

$x^{\frac{2}{3}} = 10$

Step 3

Raise each side of the equation to the power of $\frac{3}{2}$ to eliminate the fractional exponent on the left side.

${(x^{\frac{2}{3}})}^{\frac{3}{2}} = \pm 10^{\frac{3}{2}}$

Step 4

Simplify the left side.

Simplify ${(x^{\frac{2}{3}})}^{\frac{3}{2}}$ .

Multiply the exponents in ${(x^{\frac{2}{3}})}^{\frac{3}{2}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 10^{\frac{3}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 10^{\frac{3}{2}}$

Rewrite the expression.

$x^{\frac{1}{3} \cdot 3} = \pm 10^{\frac{3}{2}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x^{\frac{1}{3} \cdot 3} = \pm 10^{\frac{3}{2}}$

Rewrite the expression.

$x^{1} = \pm 10^{\frac{3}{2}}$

Simplify.

$x = \pm 10^{\frac{3}{2}}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 10^{\frac{3}{2}}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 10^{\frac{3}{2}}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 10^{\frac{3}{2}}, - 10^{\frac{3}{2}}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 10^{\frac{3}{2}}, - 10^{\frac{3}{2}}$

Decimal Form:

$x = 31.62277660 \dots, - 31.62277660 \dots$

Solve for x cube root of x^2-8=2

Related Questions

Support LCMGCF.com by disabling your adblocker.