Find the Product square root of 2x^4* square root of 8x^3

$\sqrt{2 x^{4}} \cdot \sqrt{8 x^{3}}$

Rewrite $2 x^{4}$ as ${(x^{2})}^{2} \cdot 2$ .

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Reorder $2$ and ${(x^{2})}^{2}$ .

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

Pull terms out from under the radical.

$x^{2} \sqrt{2} \cdot \sqrt{8 x^{3}}$

Rewrite $8 x^{3}$ as ${(2 x)}^{2} \cdot (2 x)$ .

Factor $4$ out of $8$ .

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

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

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

Factor out $x^{2}$ .

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

Move $2$ .

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

Rewrite $2^{2} x^{2}$ as ${(2 x)}^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

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

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

$x^{1 + 2} \sqrt{2} \cdot (2 \sqrt{2 x})$

Add $1$ and $2$ .

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

Multiply $x^{3} \sqrt{2} (2 \sqrt{2 x})$ .

Combine using the product rule for radicals.

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

Multiply $2$ by $2$ .

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

Simplify the expression.

Rewrite using the commutative property of multiplication.

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $2$ .

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

Find the Product square root of 2x^4* square root of 8x^3

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