Simplify square root of 7x^3* square root of 14x

$\sqrt{7 x^{3}} \cdot \sqrt{14 x}$

Step 1

Rewrite $7 x^{3}$ as $x^{2} \cdot (7 x)$ .

Factor out $x^{2}$ .

$\sqrt{7 (x^{2} x)} \cdot \sqrt{14 x}$

Reorder $7$ and $x^{2}$ .

$\sqrt{x^{2} \cdot 7 x} \cdot \sqrt{14 x}$

Add parentheses.

$\sqrt{x^{2} \cdot (7 x)} \cdot \sqrt{14 x}$

Step 2

Pull terms out from under the radical.

$x \sqrt{7 x} \cdot \sqrt{14 x}$

Step 3

Multiply $x \sqrt{7 x} \sqrt{14 x}$ .

Combine using the product rule for radicals.

$x \sqrt{14 x (7 x)}$

Multiply $7$ by $14$ .

$x \sqrt{98 x \cdot x}$

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

$x \sqrt{98 (x^{1} x)}$

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

$x \sqrt{98 (x^{1} x^{1})}$

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

$x \sqrt{98 x^{1 + 1}}$

Add $1$ and $1$ .

$x \sqrt{98 x^{2}}$

Step 4

Rewrite $98 x^{2}$ as ${(7 x)}^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$x \sqrt{49 (2) x^{2}}$

Rewrite $49$ as $7^{2}$ .

$x \sqrt{7^{2} \cdot 2 x^{2}}$

Move $2$ .

$x \sqrt{7^{2} x^{2} \cdot 2}$

Rewrite $7^{2} x^{2}$ as ${(7 x)}^{2}$ .

$x \sqrt{{(7 x)}^{2} \cdot 2}$

Step 5

Pull terms out from under the radical.

$x (7 x \sqrt{2})$

Step 6

Rewrite using the commutative property of multiplication.

$7 \sqrt{2} x \cdot x$

Step 7

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

Move $x$ .

$7 \sqrt{2} (x \cdot x)$

Multiply $x$ by $x$ .

$7 \sqrt{2} x^{2}$

Simplify square root of 7x^3* square root of 14x

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