Algebra Examples

$\sqrt{\frac{48}{x}}$

Step 1

Rewrite $\sqrt{\frac{48}{x}}$ as $\frac{\sqrt{48}}{\sqrt{x}}$ .

$\frac{\sqrt{48}}{\sqrt{x}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $48$ as $4^{2} \cdot 3$ .

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Step 2.1.1

Factor $16$ out of $48$ .

$\frac{\sqrt{16 (3)}}{\sqrt{x}}$

Step 2.1.2

Rewrite $16$ as $4^{2}$ .

$\frac{\sqrt{4^{2} \cdot 3}}{\sqrt{x}}$

Step 2.2

Pull terms out from under the radical.

$\frac{| 4 | \sqrt{3}}{\sqrt{x}}$

Step 2.3

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$\frac{4 \sqrt{3}}{\sqrt{x}}$

Step 3

Multiply $\frac{4 \sqrt{3}}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{4 \sqrt{3}}{\sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{4 \sqrt{3}}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{4 \sqrt{3} \sqrt{x}}{\sqrt{x} \sqrt{x}}$

Step 4.2

Raise $\sqrt{x}$ to the power of $1$ .

$\frac{4 \sqrt{3} \sqrt{x}}{{\sqrt{x}}^{1} \sqrt{x}}$

Step 4.3

Raise $\sqrt{x}$ to the power of $1$ .

$\frac{4 \sqrt{3} \sqrt{x}}{{\sqrt{x}}^{1} {\sqrt{x}}^{1}}$

Step 4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 \sqrt{3} \sqrt{x}}{{\sqrt{x}}^{1 + 1}}$

Step 4.5

Add $1$ and $1$ .

$\frac{4 \sqrt{3} \sqrt{x}}{{\sqrt{x}}^{2}}$

Step 4.6

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

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Step 4.6.1

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

$\frac{4 \sqrt{3} \sqrt{x}}{{(x^{\frac{1}{2}})}^{2}}$

Step 4.6.2

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

$\frac{4 \sqrt{3} \sqrt{x}}{x^{\frac{1}{2} \cdot 2}}$

Step 4.6.3

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

$\frac{4 \sqrt{3} \sqrt{x}}{x^{\frac{2}{2}}}$

Step 4.6.4

Cancel the common factor of $2$ .

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Step 4.6.4.1

Cancel the common factor.

$\frac{4 \sqrt{3} \sqrt{x}}{x^{\frac{2}{2}}}$

Step 4.6.4.2

Rewrite the expression.

$\frac{4 \sqrt{3} \sqrt{x}}{x^{1}}$

Step 4.6.5

Simplify.

$\frac{4 \sqrt{3} \sqrt{x}}{x}$

Step 5

Combine using the product rule for radicals.

$\frac{4 \sqrt{x \cdot 3}}{x}$

Step 6

Move $3$ to the left of $x$ .

$\frac{4 \sqrt{3 x}}{x}$