Algebra Examples

$\sqrt{3 x} = 9$

Step 1

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

${\sqrt{3 x}}^{2} = 9^{2}$

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 $\sqrt{3 x}$ as ${(3 x)}^{\frac{1}{2}}$ .

${({(3 x)}^{\frac{1}{2}})}^{2} = 9^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(3 x)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(3 x)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1.1

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

${(3 x)}^{\frac{1}{2} \cdot 2} = 9^{2}$

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.

${(3 x)}^{\frac{1}{2} \cdot 2} = 9^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(3 x)}^{1} = 9^{2}$

Step 2.2.1.2

Simplify.

$3 x = 9^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $9$ to the power of $2$ .

$3 x = 81$

Step 3

Divide each term in $3 x = 81$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 x = 81$ by $3$ .

$\frac{3 x}{3} = \frac{81}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{81}{3}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{81}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $81$ by $3$ .

$x = 27$