Basic Math Examples

$\sqrt{6 y^{2}} \cdot \sqrt{12 y^{7}}$

Step 1

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

$\sqrt{y^{2} \cdot 6} \cdot \sqrt{12 y^{7}}$

Step 2

Pull terms out from under the radical.

$y \sqrt{6} \cdot \sqrt{12 y^{7}}$

Step 3

Rewrite $12 y^{7}$ as ${(2 y^{3})}^{2} \cdot (3 y)$ .

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Step 3.1

Factor $4$ out of $12$ .

$y \sqrt{6} \cdot \sqrt{4 (3) y^{7}}$

Step 3.2

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

$y \sqrt{6} \cdot \sqrt{2^{2} \cdot 3 y^{7}}$

Step 3.3

Factor out $y^{6}$ .

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

Step 3.4

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

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

Step 3.5

Move $3$ .

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

Step 3.6

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

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

Step 3.7

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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

Step 5

Multiply $y$ by $y^{3}$ by adding the exponents.

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Step 5.1

Move $y^{3}$ .

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

Step 5.2

Multiply $y^{3}$ by $y$ .

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Step 5.2.1

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

$y^{3} y^{1} \sqrt{6} \cdot (2 \sqrt{3 y})$

Step 5.2.2

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

$y^{3 + 1} \sqrt{6} \cdot (2 \sqrt{3 y})$

Step 5.3

Add $3$ and $1$ .

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

Step 6

Multiply $y^{4} \sqrt{6} (2 \sqrt{3 y})$ .

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Step 6.1

Combine using the product rule for radicals.

$y^{4} (2 \sqrt{6 (3 y)})$

Step 6.2

Multiply $6$ by $3$ .

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

Step 7

Rewrite using the commutative property of multiplication.

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

Step 8

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

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Step 8.1

Factor $9$ out of $18$ .

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

Step 8.2

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

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

Step 8.3

Add parentheses.

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

Step 9

Pull terms out from under the radical.

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

Step 10

Multiply $3$ by $2$ .

$6 y^{4} \sqrt{2 y}$