Simplify square root of 6*4 square root of 24

$\sqrt{6} \cdot 4 \sqrt{24}$

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

Factor $4$ out of $24$ .

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

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

$\sqrt{6} \cdot (4 \sqrt{2^{2} \cdot 6})$

Pull terms out from under the radical.

$\sqrt{6} \cdot (4 (2 \sqrt{6}))$

Multiply $2$ by $4$ .

$\sqrt{6} \cdot (8 \sqrt{6})$

Multiply $\sqrt{6} (8 \sqrt{6})$ .

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

$8 ({\sqrt{6}}^{1} \sqrt{6})$

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

$8 ({\sqrt{6}}^{1} {\sqrt{6}}^{1})$

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

$8 {\sqrt{6}}^{1 + 1}$

Add $1$ and $1$ .

$8 {\sqrt{6}}^{2}$

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

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

$8 {(6^{\frac{1}{2}})}^{2}$

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

$8 \cdot 6^{\frac{1}{2} \cdot 2}$

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

$8 \cdot 6^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$8 \cdot 6^{\frac{2}{2}}$

Rewrite the expression.

$8 \cdot 6^{1}$

Evaluate the exponent.

$8 \cdot 6$

Multiply $8$ by $6$ .

$48$