Algebra Examples

$(- 2 \sqrt{20 k}) (5 \sqrt{8 k^{3}})$

Step 1

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

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Step 1.1

Factor $4$ out of $20$ .

$- 2 \sqrt{4 (5) k} (5 \sqrt{8 k^{3}})$

Step 1.2

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

$- 2 \sqrt{2^{2} \cdot 5 k} (5 \sqrt{8 k^{3}})$

Step 1.3

Add parentheses.

$- 2 \sqrt{2^{2} \cdot (5 k)} (5 \sqrt{8 k^{3}})$

$- 2 \sqrt{2^{2} \cdot (5 k)} (5 \sqrt{8 k^{3}})$

Step 2

Pull terms out from under the radical.

$- 2 (2 \sqrt{5 k}) (5 \sqrt{8 k^{3}})$

Step 3

Multiply $2$ by $- 2$ .

$- 4 \sqrt{5 k} (5 \sqrt{8 k^{3}})$

Step 4

Rewrite $8 k^{3}$ as ${(2 k)}^{2} \cdot (2 k)$ .

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Step 4.1

Factor $4$ out of $8$ .

$- 4 \sqrt{5 k} (5 \sqrt{4 (2) k^{3}})$

Step 4.2

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

$- 4 \sqrt{5 k} (5 \sqrt{2^{2} \cdot 2 k^{3}})$

Step 4.3

Factor out $k^{2}$ .

$- 4 \sqrt{5 k} (5 \sqrt{2^{2} \cdot 2 (k^{2} k)})$

Step 4.4

Move $2$ .

$- 4 \sqrt{5 k} (5 \sqrt{2^{2} k^{2} \cdot 2 k})$

Step 4.5

Rewrite $2^{2} k^{2}$ as ${(2 k)}^{2}$ .

$- 4 \sqrt{5 k} (5 \sqrt{{(2 k)}^{2} \cdot 2 k})$

Step 4.6

Add parentheses.

$- 4 \sqrt{5 k} (5 \sqrt{{(2 k)}^{2} \cdot (2 k)})$

$- 4 \sqrt{5 k} (5 \sqrt{{(2 k)}^{2} \cdot (2 k)})$

Step 5

Pull terms out from under the radical.

$- 4 \sqrt{5 k} (5 (2 k \sqrt{2 k}))$

Step 6

Multiply $2$ by $5$ .

$- 4 \sqrt{5 k} (10 (k \sqrt{2 k}))$

Step 7

Multiply $- 4 \sqrt{5 k} (10 k \sqrt{2 k})$ .

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Step 7.1

Multiply $10$ by $- 4$ .

$- 40 \sqrt{5 k} (k \sqrt{2 k})$

Step 7.2

Combine using the product rule for radicals.

$- 40 (k \sqrt{5 k (2 k)})$

Step 7.3

Multiply $2$ by $5$ .

$- 40 (k \sqrt{10 k \cdot k})$

Step 7.4

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

$- 40 (k \sqrt{10 (k^{1} k)})$

Step 7.5

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

$- 40 (k \sqrt{10 (k^{1} k^{1})})$

Step 7.6

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

$- 40 (k \sqrt{10 k^{1 + 1}})$

Step 7.7

Add $1$ and $1$ .

$- 40 (k \sqrt{10 k^{2}})$

$- 40 (k \sqrt{10 k^{2}})$

Step 8

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

$- 40 (k \sqrt{k^{2} \cdot 10})$

Step 9

Pull terms out from under the radical.

$- 40 (k (k \sqrt{10}))$

Step 10

Multiply $k$ by $k$ by adding the exponents.

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Step 10.1

Move $k$ .

$- 40 (k \cdot k \sqrt{10})$

Step 10.2

Multiply $k$ by $k$ .

$- 40 (k^{2} \sqrt{10})$

$- 40 k^{2} \sqrt{10}$

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