Basic Math Examples

$4 \sqrt{10 y} \cdot (2 \sqrt{8 y^{8}})$

Step 1

Rewrite $8 y^{8}$ as ${(2 y^{4})}^{2} \cdot 2$ .

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Step 1.1

Factor $4$ out of $8$ .

$4 \sqrt{10 y} \cdot (2 \sqrt{4 (2) y^{8}})$

Step 1.2

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

$4 \sqrt{10 y} \cdot (2 \sqrt{2^{2} \cdot 2 y^{8}})$

Step 1.3

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

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

Step 1.4

Move $2$ .

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

Step 1.5

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $2$ by $2$ .

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

Step 4

Multiply $4 \sqrt{10 y} (4 y^{4} \sqrt{2})$ .

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Step 4.1

Multiply $4$ by $4$ .

$16 \sqrt{10 y} (y^{4} \sqrt{2})$

Step 4.2

Combine using the product rule for radicals.

$16 (y^{4} \sqrt{10 y \cdot 2})$

Step 4.3

Multiply $2$ by $10$ .

$16 (y^{4} \sqrt{20 y})$

Step 5

Rewrite $20 y$ as $2^{2} \cdot (5 y)$ .

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Step 5.1

Factor $4$ out of $20$ .

$16 (y^{4} \sqrt{4 (5) y})$

Step 5.2

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

$16 (y^{4} \sqrt{2^{2} \cdot 5 y})$

Step 5.3

Add parentheses.

$16 (y^{4} \sqrt{2^{2} \cdot (5 y)})$

Step 6

Pull terms out from under the radical.

$16 (y^{4} (2 \sqrt{5 y}))$

Step 7

Simplify the expression.

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Step 7.1

Rewrite using the commutative property of multiplication.

$16 (2 y^{4} \sqrt{5 y})$

Step 7.2

Multiply $2$ by $16$ .

$32 y^{4} \sqrt{5 y}$