Simplify 3 square root of 5y*(8 square root of 10yz)

$3 \sqrt{5 y} \cdot (8 \sqrt{10 y z})$

Step 1

Multiply $3 \sqrt{5 y} (8 \sqrt{10 y z})$ .

Multiply $8$ by $3$ .

$24 \sqrt{5 y} \sqrt{10 y z}$

Combine using the product rule for radicals.

$24 \sqrt{10 y z (5 y)}$

Multiply $5$ by $10$ .

$24 \sqrt{50 y z y}$

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

$24 \sqrt{50 (y^{1} y) z}$

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

$24 \sqrt{50 (y^{1} y^{1}) z}$

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

$24 \sqrt{50 y^{1 + 1} z}$

Add $1$ and $1$ .

$24 \sqrt{50 y^{2} z}$

Step 2

Rewrite $50 y^{2} z$ as ${(5 y)}^{2} \cdot (2 z)$ .

Factor $25$ out of $50$ .

$24 \sqrt{25 (2) y^{2} z}$

Rewrite $25$ as $5^{2}$ .

$24 \sqrt{5^{2} \cdot 2 y^{2} z}$

Move $2$ .

$24 \sqrt{5^{2} y^{2} \cdot 2 z}$

Rewrite $5^{2} y^{2}$ as ${(5 y)}^{2}$ .

$24 \sqrt{{(5 y)}^{2} \cdot 2 z}$

Add parentheses.

$24 \sqrt{{(5 y)}^{2} \cdot (2 z)}$

Step 3

Pull terms out from under the radical.

$24 (5 y \sqrt{2 z})$

Step 4

Multiply $5$ by $24$ .

$120 y \sqrt{2 z}$