Algebra Examples

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

Step 1

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

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Step 1.1

Multiply $8$ by $3$ .

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

Step 1.2

Combine using the product rule for radicals.

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

Step 1.3

Multiply $5$ by $10$ .

$24 \sqrt{50 y z y}$

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

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

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

Step 1.7

Add $1$ and $1$ .

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

Step 2

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

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Step 2.1

Factor $25$ out of $50$ .

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

Step 2.2

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

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

Step 2.3

Move $2$ .

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

Step 2.4

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

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

Step 2.5

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 $24$ .

$120 y \sqrt{2 z}$