Basic Math Examples

$w \sqrt{54 y^{3}} + 5 y \sqrt{96 y w^{2}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $54 y^{3}$ as ${(3 y)}^{2} \cdot (6 y)$ .

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Step 1.1.1

Factor $9$ out of $54$ .

$w \sqrt{9 (6) y^{3}} + 5 y \sqrt{96 y w^{2}}$

Step 1.1.2

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

$w \sqrt{3^{2} \cdot 6 y^{3}} + 5 y \sqrt{96 y w^{2}}$

Step 1.1.3

Factor out $y^{2}$ .

$w \sqrt{3^{2} \cdot 6 (y^{2} y)} + 5 y \sqrt{96 y w^{2}}$

Step 1.1.4

Move $6$ .

$w \sqrt{3^{2} y^{2} \cdot 6 y} + 5 y \sqrt{96 y w^{2}}$

Step 1.1.5

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

$w \sqrt{{(3 y)}^{2} \cdot 6 y} + 5 y \sqrt{96 y w^{2}}$

Step 1.1.6

Add parentheses.

$w \sqrt{{(3 y)}^{2} \cdot (6 y)} + 5 y \sqrt{96 y w^{2}}$

Step 1.2

Pull terms out from under the radical.

$w (3 y \sqrt{6 y}) + 5 y \sqrt{96 y w^{2}}$

Step 1.3

Rewrite using the commutative property of multiplication.

$3 w y \sqrt{6 y} + 5 y \sqrt{96 y w^{2}}$

Step 1.4

Rewrite $96 y w^{2}$ as ${(4 w)}^{2} \cdot (6 y)$ .

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Step 1.4.1

Factor $16$ out of $96$ .

$3 w y \sqrt{6 y} + 5 y \sqrt{16 (6) y w^{2}}$

Step 1.4.2

Rewrite $16$ as $4^{2}$ .

$3 w y \sqrt{6 y} + 5 y \sqrt{4^{2} \cdot 6 y w^{2}}$

Step 1.4.3

Move $y$ .

$3 w y \sqrt{6 y} + 5 y \sqrt{4^{2} \cdot 6 w^{2} y}$

Step 1.4.4

Move $6$ .

$3 w y \sqrt{6 y} + 5 y \sqrt{4^{2} w^{2} \cdot 6 y}$

Step 1.4.5

Rewrite $4^{2} w^{2}$ as ${(4 w)}^{2}$ .

$3 w y \sqrt{6 y} + 5 y \sqrt{{(4 w)}^{2} \cdot 6 y}$

Step 1.4.6

Add parentheses.

$3 w y \sqrt{6 y} + 5 y \sqrt{{(4 w)}^{2} \cdot (6 y)}$

Step 1.5

Pull terms out from under the radical.

$3 w y \sqrt{6 y} + 5 y (4 w \sqrt{6 y})$

Step 1.6

Multiply $4$ by $5$ .

$3 w y \sqrt{6 y} + 20 y (w \sqrt{6 y})$

Step 2

Add $3 w y \sqrt{6 y}$ and $20 y (w \sqrt{6 y})$ .

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Step 2.1

Move $y$ .

$3 w y \sqrt{6 y} + 20 w y \sqrt{6 y}$

Step 2.2

Add $3 w y \sqrt{6 y}$ and $20 w y \sqrt{6 y}$ .

$23 w y \sqrt{6 y}$