Simplify square root of 14q*(2 square root of 4q)

$\sqrt{14 q} \cdot (2 \sqrt{4 q})$

Step 1

Simplify the expression.

Rewrite using the commutative property of multiplication.

$2 \sqrt{14 q} \sqrt{4 q}$

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

$2 \sqrt{14 q} \sqrt{2^{2} q}$

Step 2

Pull terms out from under the radical.

$2 \sqrt{14 q} (2 \sqrt{q})$

Step 3

Multiply $2 \sqrt{14 q} (2 \sqrt{q})$ .

Multiply $2$ by $2$ .

$4 \sqrt{14 q} \sqrt{q}$

Combine using the product rule for radicals.

$4 \sqrt{q (14 q)}$

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

$4 \sqrt{14 (q^{1} q)}$

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

$4 \sqrt{14 (q^{1} q^{1})}$

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

$4 \sqrt{14 q^{1 + 1}}$

Add $1$ and $1$ .

$4 \sqrt{14 q^{2}}$

Step 4

Reorder $14$ and $q^{2}$ .

$4 \sqrt{q^{2} \cdot 14}$

Step 5

Pull terms out from under the radical.

$4 q \sqrt{14}$