Algebra Examples

$4 \sqrt{10 n^{2}} \cdot - 3 \sqrt{8 n}$

Step 1

Reorder $10$ and $n^{2}$ .

$4 \sqrt{n^{2} \cdot 10} \cdot (- 3 \sqrt{8 n})$

Step 2

Pull terms out from under the radical.

$4 (n \sqrt{10}) \cdot (- 3 \sqrt{8 n})$

Step 3

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

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Step 3.1

Factor $4$ out of $8$ .

$4 n \sqrt{10} \cdot (- 3 \sqrt{4 (2) n})$

Step 3.2

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

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

Step 3.3

Add parentheses.

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

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

Step 4

Pull terms out from under the radical.

$4 n \sqrt{10} \cdot (- 3 (2 \sqrt{2 n}))$

Step 5

Multiply $2$ by $- 3$ .

$4 n \sqrt{10} \cdot (- 6 \sqrt{2 n})$

Step 6

Multiply $4 n \sqrt{10} (- 6 \sqrt{2 n})$ .

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Step 6.1

Multiply $- 6$ by $4$ .

$- 24 n \sqrt{10} \sqrt{2 n}$

Step 6.2

Combine using the product rule for radicals.

$- 24 n \sqrt{2 n \cdot 10}$

Step 6.3

Multiply $10$ by $2$ .

$- 24 n \sqrt{20 n}$

$- 24 n \sqrt{20 n}$

Step 7

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

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Step 7.1

Factor $4$ out of $20$ .

$- 24 n \sqrt{4 (5) n}$

Step 7.2

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

$- 24 n \sqrt{2^{2} \cdot 5 n}$

Step 7.3

Add parentheses.

$- 24 n \sqrt{2^{2} \cdot (5 n)}$

$- 24 n \sqrt{2^{2} \cdot (5 n)}$

Step 8

Pull terms out from under the radical.

$- 24 n (2 \sqrt{5 n})$

Step 9

Multiply $2$ by $- 24$ .

$- 48 n \sqrt{5 n}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$