Basic Math Examples

$\sqrt{3 y^{3}} \cdot (3 \sqrt{5 y^{2}})$

Step 1

Rewrite using the commutative property of multiplication.

$3 \sqrt{3 y^{3}} \sqrt{5 y^{2}}$

Step 2

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

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Step 2.1

Factor out $y^{2}$ .

$3 \sqrt{3 (y^{2} y)} \sqrt{5 y^{2}}$

Step 2.2

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

$3 \sqrt{y^{2} \cdot 3 y} \sqrt{5 y^{2}}$

Step 2.3

Add parentheses.

$3 \sqrt{y^{2} \cdot (3 y)} \sqrt{5 y^{2}}$

$3 \sqrt{y^{2} \cdot (3 y)} \sqrt{5 y^{2}}$

Step 3

Pull terms out from under the radical.

$3 (y \sqrt{3 y}) \sqrt{5 y^{2}}$

Step 4

Reorder $5$ and $y^{2}$ .

$3 y \sqrt{3 y} \sqrt{y^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

$3 y \sqrt{3 y} (y \sqrt{5})$

Step 6

Multiply $y$ by $y$ by adding the exponents.

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Step 6.1

Move $y$ .

$3 (y \cdot y) \sqrt{3 y} \sqrt{5}$

Step 6.2

Multiply $y$ by $y$ .

$3 y^{2} \sqrt{3 y} \sqrt{5}$

$3 y^{2} \sqrt{3 y} \sqrt{5}$

Step 7

Multiply $3 y^{2} \sqrt{3 y} \sqrt{5}$ .

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Step 7.1

Combine using the product rule for radicals.

$3 y^{2} \sqrt{5 (3 y)}$

Step 7.2

Multiply $5$ by $3$ .

$3 y^{2} \sqrt{15 y}$

$3 y^{2} \sqrt{15 y}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$