Simplify square root of 3x* square root of 8x^3

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

Step 1

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

Factor $4$ out of $8$ .

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

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

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

Factor out $x^{2}$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

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

Combine using the product rule for radicals.

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

Multiply $2$ by $3$ .

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

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

$2 (x \sqrt{6 (x^{1} x)})$

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

$2 (x \sqrt{6 (x^{1} x^{1})})$

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

$2 (x \sqrt{6 x^{1 + 1}})$

Add $1$ and $1$ .

$2 (x \sqrt{6 x^{2}})$

Step 5

Reorder $6$ and $x^{2}$ .

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

Step 6

Pull terms out from under the radical.

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

Step 7

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

$2 (x^{2} \sqrt{6})$

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

Simplify square root of 3x* square root of 8x^3

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