Basic Math Examples

$\sqrt{18 y^{2}} \cdot (4 \sqrt{3 y^{2}})$

Step 1

Rewrite using the commutative property of multiplication.

$4 \sqrt{18 y^{2}} \sqrt{3 y^{2}}$

Step 2

Rewrite $18 y^{2}$ as ${(3 y)}^{2} \cdot 2$ .

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Step 2.1

Factor $9$ out of $18$ .

$4 \sqrt{9 (2) y^{2}} \sqrt{3 y^{2}}$

Step 2.2

Rewrite $9$ as $3^{2}$ .

$4 \sqrt{3^{2} \cdot 2 y^{2}} \sqrt{3 y^{2}}$

Step 2.3

Move $2$ .

$4 \sqrt{3^{2} y^{2} \cdot 2} \sqrt{3 y^{2}}$

Step 2.4

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

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

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

Step 3

Pull terms out from under the radical.

$4 (3 y \sqrt{2}) \sqrt{3 y^{2}}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $3$ by $4$ .

$12 (y \sqrt{2}) \sqrt{3 y^{2}}$

Step 4.2

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

$12 y \sqrt{2} \sqrt{y^{2} \cdot 3}$

$12 y \sqrt{2} \sqrt{y^{2} \cdot 3}$

Step 5

Pull terms out from under the radical.

$12 y \sqrt{2} (y \sqrt{3})$

Step 6

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

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Step 6.1

Move $y$ .

$12 (y \cdot y) \sqrt{2} \sqrt{3}$

Step 6.2

Multiply $y$ by $y$ .

$12 y^{2} \sqrt{2} \sqrt{3}$

$12 y^{2} \sqrt{2} \sqrt{3}$

Step 7

Multiply $12 y^{2} \sqrt{2} \sqrt{3}$ .

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Step 7.1

Combine using the product rule for radicals.

$12 y^{2} \sqrt{3 \cdot 2}$

Step 7.2

Multiply $3$ by $2$ .

$12 y^{2} \sqrt{6}$

$12 y^{2} \sqrt{6}$

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