Basic Math Examples

$\sqrt{2 y^{3}} \cdot \sqrt{6 y^{2}} \cdot \sqrt{10 y}$

Step 1

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

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Step 1.1

Factor out $y^{2}$ .

$\sqrt{2 (y^{2} y)} \cdot \sqrt{6 y^{2}} \cdot \sqrt{10 y}$

Step 1.2

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

$\sqrt{y^{2} \cdot 2 y} \cdot \sqrt{6 y^{2}} \cdot \sqrt{10 y}$

Step 1.3

Add parentheses.

$\sqrt{y^{2} \cdot (2 y)} \cdot \sqrt{6 y^{2}} \cdot \sqrt{10 y}$

Step 2

Pull terms out from under the radical.

$y \sqrt{2 y} \cdot \sqrt{6 y^{2}} \cdot \sqrt{10 y}$

Step 3

Reorder $6$ and $y^{2}$ .

$y \sqrt{2 y} \cdot \sqrt{y^{2} \cdot 6} \cdot \sqrt{10 y}$

Step 4

Pull terms out from under the radical.

$y \sqrt{2 y} \cdot (y \sqrt{6}) \cdot \sqrt{10 y}$

Step 5

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

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Step 5.1

Move $y$ .

$y \cdot y \sqrt{2 y} \cdot \sqrt{6} \cdot \sqrt{10 y}$

Step 5.2

Multiply $y$ by $y$ .

$y^{2} \sqrt{2 y} \cdot \sqrt{6} \cdot \sqrt{10 y}$

Step 6

Multiply $y^{2} \sqrt{2 y} \sqrt{6}$ .

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Step 6.1

Combine using the product rule for radicals.

$y^{2} \sqrt{6 (2 y)} \cdot \sqrt{10 y}$

Step 6.2

Multiply $6$ by $2$ .

$y^{2} \sqrt{12 y} \cdot \sqrt{10 y}$

Step 7

Rewrite $12 y$ as $2^{2} \cdot (3 y)$ .

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Step 7.1

Factor $4$ out of $12$ .

$y^{2} \sqrt{4 (3) y} \cdot \sqrt{10 y}$

Step 7.2

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

$y^{2} \sqrt{2^{2} \cdot 3 y} \cdot \sqrt{10 y}$

Step 7.3

Add parentheses.

$y^{2} \sqrt{2^{2} \cdot (3 y)} \cdot \sqrt{10 y}$

Step 8

Pull terms out from under the radical.

$y^{2} (2 \sqrt{3 y}) \cdot \sqrt{10 y}$

Step 9

Rewrite using the commutative property of multiplication.

$2 y^{2} \sqrt{3 y} \cdot \sqrt{10 y}$

Step 10

Multiply $2 y^{2} \sqrt{3 y} \sqrt{10 y}$ .

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Step 10.1

Combine using the product rule for radicals.

$2 y^{2} \sqrt{10 y (3 y)}$

Step 10.2

Multiply $3$ by $10$ .

$2 y^{2} \sqrt{30 y \cdot y}$

Step 10.3

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

$2 y^{2} \sqrt{30 (y^{1} y)}$

Step 10.4

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

$2 y^{2} \sqrt{30 (y^{1} y^{1})}$

Step 10.5

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

$2 y^{2} \sqrt{30 y^{1 + 1}}$

Step 10.6

Add $1$ and $1$ .

$2 y^{2} \sqrt{30 y^{2}}$

Step 11

Reorder $30$ and $y^{2}$ .

$2 y^{2} \sqrt{y^{2} \cdot 30}$

Step 12

Pull terms out from under the radical.

$2 y^{2} (y \sqrt{30})$

Step 13

Multiply $y^{2}$ by $y$ by adding the exponents.

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Step 13.1

Move $y$ .

$2 (y \cdot y^{2}) \sqrt{30}$

Step 13.2

Multiply $y$ by $y^{2}$ .

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Step 13.2.1

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

$2 (y^{1} y^{2}) \sqrt{30}$

Step 13.2.2

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

$2 y^{1 + 2} \sqrt{30}$

Step 13.3

Add $1$ and $2$ .

$2 y^{3} \sqrt{30}$