Simplify 4 square root of 2x*(3 square root of 8x)

$4 \sqrt{2 x} \cdot (3 \sqrt{8 x})$

Step 1

Rewrite $8 x$ as $2^{2} \cdot (2 x)$ .

Factor $4$ out of $8$ .

$4 \sqrt{2 x} \cdot (3 \sqrt{4 (2) x})$

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$4 \sqrt{2 x} \cdot (3 (2 \sqrt{2 x}))$

Step 3

Multiply $2$ by $3$ .

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

Step 4

Multiply $4 \sqrt{2 x} (6 \sqrt{2 x})$ .

Multiply $6$ by $4$ .

$24 \sqrt{2 x} \sqrt{2 x}$

Raise $\sqrt{2 x}$ to the power of $1$ .

$24 ({\sqrt{2 x}}^{1} \sqrt{2 x})$

Raise $\sqrt{2 x}$ to the power of $1$ .

$24 ({\sqrt{2 x}}^{1} {\sqrt{2 x}}^{1})$

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

$24 {\sqrt{2 x}}^{1 + 1}$

Add $1$ and $1$ .

$24 {\sqrt{2 x}}^{2}$

Step 5

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

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

$24 {({(2 x)}^{\frac{1}{2}})}^{2}$

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

$24 {(2 x)}^{\frac{1}{2} \cdot 2}$

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

$24 {(2 x)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$24 {(2 x)}^{\frac{2}{2}}$

Rewrite the expression.

$24 {(2 x)}^{1}$

Simplify.

$24 (2 x)$

Step 6

Multiply $2$ by $24$ .

$48 x$