Simplify square root of 16x^3 square root of 4x

$\sqrt{16 x^{3}} \sqrt{4 x}$

Step 1

Rewrite $16 x^{3}$ as ${(4 x)}^{2} x$ .

Rewrite $16$ as $4^{2}$ .

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

Factor out $x^{2}$ .

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

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

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

Step 2

Pull terms out from under the radical.

$4 x \sqrt{x} \sqrt{4 x}$

Step 3

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

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

Multiply $2$ by $4$ .

$8 x \sqrt{x} \sqrt{x}$

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

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

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

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

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

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

Add $1$ and $1$ .

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

Step 6

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$8 x \cdot x^{1}$

Simplify.

$8 x \cdot x$

Step 7

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

Move $x$ .

$8 (x \cdot x)$

Multiply $x$ by $x$ .

$8 x^{2}$

Simplify square root of 16x^3 square root of 4x

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