Take the square root of each side of the equation to set up the solution for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math>

Remove the perfect root factor <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>8</mn></mstyle></math> under the radical to solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>48</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>4</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>3</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>48</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>4</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

First, use the positive value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the first solution.

Add <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> to both sides of the equation.

Next, use the negative value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the second solution.

Add <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> to both sides of the equation.

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

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

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