Evaluate 1/3* square root of 6* square root of 24

$\frac{1}{3} \cdot \sqrt{6} \cdot \sqrt{24}$

Step 1

Combine $\frac{1}{3}$ and $\sqrt{6}$ .

$\frac{\sqrt{6}}{3} \cdot \sqrt{24}$

Step 2

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$\frac{\sqrt{6}}{3} \cdot \sqrt{4 (6)}$

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

$\frac{\sqrt{6}}{3} \cdot \sqrt{2^{2} \cdot 6}$

Step 3

Pull terms out from under the radical.

$\frac{\sqrt{6}}{3} \cdot (2 \sqrt{6})$

Step 4

Multiply $\frac{\sqrt{6}}{3} (2 \sqrt{6})$ .

Combine $2$ and $\frac{\sqrt{6}}{3}$ .

$\frac{2 \sqrt{6}}{3} \sqrt{6}$

Combine $\frac{2 \sqrt{6}}{3}$ and $\sqrt{6}$ .

$\frac{2 \sqrt{6} \sqrt{6}}{3}$

Raise $\sqrt{6}$ to the power of $1$ .

$\frac{2 ({\sqrt{6}}^{1} \sqrt{6})}{3}$

Raise $\sqrt{6}$ to the power of $1$ .

$\frac{2 ({\sqrt{6}}^{1} {\sqrt{6}}^{1})}{3}$

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

$\frac{2 {\sqrt{6}}^{1 + 1}}{3}$

Add $1$ and $1$ .

$\frac{2 {\sqrt{6}}^{2}}{3}$

Step 5

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$\frac{2 {(6^{\frac{1}{2}})}^{2}}{3}$

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

$\frac{2 \cdot 6^{\frac{1}{2} \cdot 2}}{3}$

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

$\frac{2 \cdot 6^{\frac{2}{2}}}{3}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \cdot 6^{\frac{2}{2}}}{3}$

Rewrite the expression.

$\frac{2 \cdot 6^{1}}{3}$

Evaluate the exponent.

$\frac{2 \cdot 6}{3}$

Step 6

Simplify the expression.

Multiply $2$ by $6$ .

$\frac{12}{3}$

Divide $12$ by $3$ .

$4$

Evaluate 1/3* square root of 6* square root of 24

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