Simplify square root of 2p*-4 square root of 3p^3

$\sqrt{2 p} \cdot - 4 \sqrt{3 p^{3}}$

Step 1

Rewrite using the commutative property of multiplication.

$- 4 \sqrt{2 p} \sqrt{3 p^{3}}$

Step 2

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

Factor out $p^{2}$ .

$- 4 \sqrt{2 p} \sqrt{3 (p^{2} p)}$

Reorder $3$ and $p^{2}$ .

$- 4 \sqrt{2 p} \sqrt{p^{2} \cdot 3 p}$

Add parentheses.

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

Step 3

Pull terms out from under the radical.

$- 4 \sqrt{2 p} (p \sqrt{3 p})$

Step 4

Multiply $- 4 \sqrt{2 p} (p \sqrt{3 p})$ .

Combine using the product rule for radicals.

$- 4 (p \sqrt{2 p (3 p)})$

Multiply $3$ by $2$ .

$- 4 (p \sqrt{6 p \cdot p})$

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

$- 4 (p \sqrt{6 (p^{1} p)})$

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

$- 4 (p \sqrt{6 (p^{1} p^{1})})$

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

$- 4 (p \sqrt{6 p^{1 + 1}})$

Add $1$ and $1$ .

$- 4 (p \sqrt{6 p^{2}})$

Step 5

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

$- 4 (p \sqrt{p^{2} \cdot 6})$

Step 6

Pull terms out from under the radical.

$- 4 (p (p \sqrt{6}))$

Step 7

Multiply $p$ by $p$ by adding the exponents.

Move $p$ .

$- 4 (p \cdot p \sqrt{6})$

Multiply $p$ by $p$ .

$- 4 (p^{2} \sqrt{6})$

$- 4 p^{2} \sqrt{6}$