Algebra Examples

$2 \sqrt{25 y^{8}} \cdot 4 \sqrt{6 y^{3}}$

Step 1

Rewrite $25 y^{8}$ as ${(5 y^{4})}^{2}$ .

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

Step 2

Pull terms out from under the radical, assuming positive real numbers.

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

Step 3

Multiply $5$ by $2$ .

$10 y^{4} \cdot (4 \sqrt{6 y^{3}})$

Step 4

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

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Step 4.1

Factor out $y^{2}$ .

$10 y^{4} \cdot (4 \sqrt{6 (y^{2} y)})$

Step 4.2

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

$10 y^{4} \cdot (4 \sqrt{y^{2} \cdot 6 y})$

Step 4.3

Add parentheses.

$10 y^{4} \cdot (4 \sqrt{y^{2} \cdot (6 y)})$

Step 5

Pull terms out from under the radical.

$10 y^{4} \cdot (4 (y \sqrt{6 y}))$

Step 6

Multiply $y^{4}$ by $y$ by adding the exponents.

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Step 6.1

Move $y$ .

$10 (y \cdot y^{4}) \cdot (4 (\sqrt{6 y}))$

Step 6.2

Multiply $y$ by $y^{4}$ .

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Step 6.2.1

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

$10 (y^{1} y^{4}) \cdot (4 (\sqrt{6 y}))$

Step 6.2.2

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

$10 y^{1 + 4} \cdot (4 (\sqrt{6 y}))$

Step 6.3

Add $1$ and $4$ .

$10 y^{5} \cdot (4 (\sqrt{6 y}))$

Step 7

Multiply $4$ by $10$ .

$40 y^{5} \sqrt{6 y}$