Algebra Examples

$2 = \sqrt{8 x}$

Step 1

Rewrite the equation as $\sqrt{8 x} = 2$ .

$\sqrt{8 x} = 2$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{8 x}}^{2} = 2^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{8 x}$ as ${(8 x)}^{\frac{1}{2}}$ .

${({(8 x)}^{\frac{1}{2}})}^{2} = 2^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(8 x)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(8 x)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(8 x)}^{\frac{1}{2} \cdot 2} = 2^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(8 x)}^{\frac{1}{2} \cdot 2} = 2^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(8 x)}^{1} = 2^{2}$

Step 3.2.1.2

Simplify.

$8 x = 2^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $2$ to the power of $2$ .

$8 x = 4$

Step 4

Divide each term in $8 x = 4$ by $8$ and simplify.

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Step 4.1

Divide each term in $8 x = 4$ by $8$ .

$\frac{8 x}{8} = \frac{4}{8}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $8$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{4}{8}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{4}{8}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $4$ and $8$ .

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Step 4.3.1.1

Factor $4$ out of $4$ .

$x = \frac{4 (1)}{8}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $4$ out of $8$ .

$x = \frac{4 \cdot 1}{4 \cdot 2}$

Step 4.3.1.2.2

Cancel the common factor.

$x = \frac{4 \cdot 1}{4 \cdot 2}$

Step 4.3.1.2.3

Rewrite the expression.

$x = \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}$

Decimal Form:

$x = 0.5$