Precalculus Examples

$\sqrt{8 x - 1} = 3$

Step 1

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

${\sqrt{8 x - 1}}^{2} = 3^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

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

${({(8 x - 1)}^{\frac{1}{2}})}^{2} = 3^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

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

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Step 2.2.1.1.1

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

${(8 x - 1)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

${(8 x - 1)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(8 x - 1)}^{1} = 3^{2}$

Step 2.2.1.2

Simplify.

$8 x - 1 = 3^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $3$ to the power of $2$ .

$8 x - 1 = 9$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Add $1$ to both sides of the equation.

$8 x = 9 + 1$

Step 3.1.2

Add $9$ and $1$ .

$8 x = 10$

Step 3.2

Divide each term in $8 x = 10$ by $8$ and simplify.

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Step 3.2.1

Divide each term in $8 x = 10$ by $8$ .

$\frac{8 x}{8} = \frac{10}{8}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $8$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{10}{8}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{10}{8}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Cancel the common factor of $10$ and $8$ .

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Step 3.2.3.1.1

Factor $2$ out of $10$ .

$x = \frac{2 (5)}{8}$

Step 3.2.3.1.2

Cancel the common factors.

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Step 3.2.3.1.2.1

Factor $2$ out of $8$ .

$x = \frac{2 \cdot 5}{2 \cdot 4}$

Step 3.2.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 5}{2 \cdot 4}$

Step 3.2.3.1.2.3

Rewrite the expression.

$x = \frac{5}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{4}$

Decimal Form:

$x = 1.25$

Mixed Number Form:

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