Algebra Examples

${(3 \sqrt{3})}^{2} = \sqrt{x}$

Step 1

Simplify ${(3 \sqrt{3})}^{2}$ .

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Step 1.1

Simplify the expression.

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Step 1.1.1

Apply the product rule to $3 \sqrt{3}$ .

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

Step 1.1.2

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

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

Step 1.2

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 1.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

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

Step 1.2.2

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

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

Step 1.2.3

Combine $\frac{1}{2}$ and $2$ .

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

Step 1.2.4

Cancel the common factor of $2$ .

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Step 1.2.4.1

Cancel the common factor.

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

Step 1.2.4.2

Rewrite the expression.

$9 \cdot 3^{1} = \sqrt{x}$

Step 1.2.5

Evaluate the exponent.

$9 \cdot 3 = \sqrt{x}$

Step 1.3

Multiply $9$ by $3$ .

$27 = \sqrt{x}$

Step 2

Rewrite the equation as $\sqrt{x} = 27$ .

$\sqrt{x} = 27$

Step 3

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

${\sqrt{x}}^{2} = 27^{2}$

Step 4

Simplify each side of the equation.

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Step 4.1

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

${(x^{\frac{1}{2}})}^{2} = 27^{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

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

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Step 4.2.1.1

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

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Step 4.2.1.1.1

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

$x^{\frac{1}{2} \cdot 2} = 27^{2}$

Step 4.2.1.1.2

Cancel the common factor of $2$ .

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Step 4.2.1.1.2.1

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 27^{2}$

Step 4.2.1.1.2.2

Rewrite the expression.

$x^{1} = 27^{2}$

Step 4.2.1.2

Simplify.

$x = 27^{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Raise $27$ to the power of $2$ .

$x = 729$