Algebra Examples

$y \sqrt{2 y^{3}} - 3 \sqrt{8 y^{5}} + 3 y \sqrt{72 y^{3}}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor out $y^{2}$ .

$y \sqrt{2 (y^{2} y)} - 3 \sqrt{8 y^{5}} + 3 y \sqrt{72 y^{3}}$

Step 1.1.2

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

$y \sqrt{y^{2} \cdot 2 y} - 3 \sqrt{8 y^{5}} + 3 y \sqrt{72 y^{3}}$

Step 1.1.3

Add parentheses.

$y \sqrt{y^{2} \cdot (2 y)} - 3 \sqrt{8 y^{5}} + 3 y \sqrt{72 y^{3}}$

Step 1.2

Pull terms out from under the radical.

$y (y \sqrt{2 y}) - 3 \sqrt{8 y^{5}} + 3 y \sqrt{72 y^{3}}$

Step 1.3

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

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Step 1.3.1

Move $y$ .

$y \cdot y \sqrt{2 y} - 3 \sqrt{8 y^{5}} + 3 y \sqrt{72 y^{3}}$

Step 1.3.2

Multiply $y$ by $y$ .

$y^{2} \sqrt{2 y} - 3 \sqrt{8 y^{5}} + 3 y \sqrt{72 y^{3}}$

Step 1.4

Rewrite $8 y^{5}$ as ${(2 y^{2})}^{2} \cdot (2 y)$ .

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Step 1.4.1

Factor $4$ out of $8$ .

$y^{2} \sqrt{2 y} - 3 \sqrt{4 (2) y^{5}} + 3 y \sqrt{72 y^{3}}$

Step 1.4.2

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

$y^{2} \sqrt{2 y} - 3 \sqrt{2^{2} \cdot 2 y^{5}} + 3 y \sqrt{72 y^{3}}$

Step 1.4.3

Factor out $y^{4}$ .

$y^{2} \sqrt{2 y} - 3 \sqrt{2^{2} \cdot 2 (y^{4} y)} + 3 y \sqrt{72 y^{3}}$

Step 1.4.4

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

$y^{2} \sqrt{2 y} - 3 \sqrt{2^{2} \cdot 2 ({(y^{2})}^{2} y)} + 3 y \sqrt{72 y^{3}}$

Step 1.4.5

Move $2$ .

$y^{2} \sqrt{2 y} - 3 \sqrt{2^{2} {(y^{2})}^{2} \cdot 2 y} + 3 y \sqrt{72 y^{3}}$

Step 1.4.6

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

$y^{2} \sqrt{2 y} - 3 \sqrt{{(2 y^{2})}^{2} \cdot 2 y} + 3 y \sqrt{72 y^{3}}$

Step 1.4.7

Add parentheses.

$y^{2} \sqrt{2 y} - 3 \sqrt{{(2 y^{2})}^{2} \cdot (2 y)} + 3 y \sqrt{72 y^{3}}$

Step 1.5

Pull terms out from under the radical.

$y^{2} \sqrt{2 y} - 3 (2 y^{2} \sqrt{2 y}) + 3 y \sqrt{72 y^{3}}$

Step 1.6

Multiply $2$ by $- 3$ .

$y^{2} \sqrt{2 y} - 6 (y^{2} \sqrt{2 y}) + 3 y \sqrt{72 y^{3}}$

Step 1.7

Rewrite $72 y^{3}$ as ${(6 y)}^{2} \cdot (2 y)$ .

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Step 1.7.1

Factor $36$ out of $72$ .

$y^{2} \sqrt{2 y} - 6 y^{2} \sqrt{2 y} + 3 y \sqrt{36 (2) y^{3}}$

Step 1.7.2

Rewrite $36$ as $6^{2}$ .

$y^{2} \sqrt{2 y} - 6 y^{2} \sqrt{2 y} + 3 y \sqrt{6^{2} \cdot 2 y^{3}}$

Step 1.7.3

Factor out $y^{2}$ .

$y^{2} \sqrt{2 y} - 6 y^{2} \sqrt{2 y} + 3 y \sqrt{6^{2} \cdot 2 (y^{2} y)}$

Step 1.7.4

Move $2$ .

$y^{2} \sqrt{2 y} - 6 y^{2} \sqrt{2 y} + 3 y \sqrt{6^{2} y^{2} \cdot 2 y}$

Step 1.7.5

Rewrite $6^{2} y^{2}$ as ${(6 y)}^{2}$ .

$y^{2} \sqrt{2 y} - 6 y^{2} \sqrt{2 y} + 3 y \sqrt{{(6 y)}^{2} \cdot 2 y}$

Step 1.7.6

Add parentheses.

$y^{2} \sqrt{2 y} - 6 y^{2} \sqrt{2 y} + 3 y \sqrt{{(6 y)}^{2} \cdot (2 y)}$

Step 1.8

Pull terms out from under the radical.

$y^{2} \sqrt{2 y} - 6 y^{2} \sqrt{2 y} + 3 y (6 y \sqrt{2 y})$

Step 1.9

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

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Step 1.9.1

Move $y$ .

$y^{2} \sqrt{2 y} - 6 y^{2} \sqrt{2 y} + 3 (y \cdot y) (6 \sqrt{2 y})$

Step 1.9.2

Multiply $y$ by $y$ .

$y^{2} \sqrt{2 y} - 6 y^{2} \sqrt{2 y} + 3 y^{2} (6 \sqrt{2 y})$

Step 1.10

Multiply $6$ by $3$ .

$y^{2} \sqrt{2 y} - 6 y^{2} \sqrt{2 y} + 18 y^{2} \sqrt{2 y}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $6 y^{2} \sqrt{2 y}$ from $y^{2} \sqrt{2 y}$ .

$- 5 y^{2} \sqrt{2 y} + 18 y^{2} \sqrt{2 y}$

Step 2.2

Add $- 5 y^{2} \sqrt{2 y}$ and $18 y^{2} \sqrt{2 y}$ .

$13 y^{2} \sqrt{2 y}$