Simplify square root of (5x)/12

$\sqrt{\frac{5 x}{12}}$

Step 1

Rewrite $\frac{5 x}{12}$ as ${(\frac{1}{2})}^{2} \frac{5 x}{3}$ .

Factor the perfect power $1^{2}$ out of $5 x$ .

$\sqrt{\frac{1^{2} (5 x)}{12}}$

Factor the perfect power $2^{2}$ out of $12$ .

$\sqrt{\frac{1^{2} (5 x)}{2^{2} \cdot 3}}$

Rearrange the fraction $\frac{1^{2} (5 x)}{2^{2} \cdot 3}$ .

$\sqrt{{(\frac{1}{2})}^{2} \frac{5 x}{3}}$

Step 2

Pull terms out from under the radical.

$\frac{1}{2} \sqrt{\frac{5 x}{3}}$

Step 3

Rewrite $\sqrt{\frac{5 x}{3}}$ as $\frac{\sqrt{5 x}}{\sqrt{3}}$ .

$\frac{1}{2} \cdot \frac{\sqrt{5 x}}{\sqrt{3}}$

Step 4

Multiply $\frac{\sqrt{5 x}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{1}{2} (\frac{\sqrt{5 x}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}})$

Step 5

Combine and simplify the denominator.

Multiply $\frac{\sqrt{5 x}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{1}{2} \cdot \frac{\sqrt{5 x} \sqrt{3}}{\sqrt{3} \sqrt{3}}$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{1}{2} \cdot \frac{\sqrt{5 x} \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{1}{2} \cdot \frac{\sqrt{5 x} \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

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

$\frac{1}{2} \cdot \frac{\sqrt{5 x} \sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{1}{2} \cdot \frac{\sqrt{5 x} \sqrt{3}}{{\sqrt{3}}^{2}}$

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

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

$\frac{1}{2} \cdot \frac{\sqrt{5 x} \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}$

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

$\frac{1}{2} \cdot \frac{\sqrt{5 x} \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

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

$\frac{1}{2} \cdot \frac{\sqrt{5 x} \sqrt{3}}{3^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{1}{2} \cdot \frac{\sqrt{5 x} \sqrt{3}}{3^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{1}{2} \cdot \frac{\sqrt{5 x} \sqrt{3}}{3^{1}}$

Evaluate the exponent.

$\frac{1}{2} \cdot \frac{\sqrt{5 x} \sqrt{3}}{3}$

Step 6

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{1}{2} \cdot \frac{\sqrt{5 x \cdot 3}}{3}$

Multiply $3$ by $5$ .

$\frac{1}{2} \cdot \frac{\sqrt{15 x}}{3}$

Step 7

Multiply $\frac{1}{2} \cdot \frac{\sqrt{15 x}}{3}$ .

Multiply $\frac{1}{2}$ by $\frac{\sqrt{15 x}}{3}$ .

$\frac{\sqrt{15 x}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$\frac{\sqrt{15 x}}{6}$

Simplify square root of (5x)/12

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