Basic Math Examples

$(- 2 \sqrt{44}) (3 \sqrt{28})$

Step 1

Rewrite $44$ as $2^{2} \cdot 11$ .

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Step 1.1

Factor $4$ out of $44$ .

$- 2 \sqrt{4 (11)} (3 \sqrt{28})$

Step 1.2

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

$- 2 \sqrt{2^{2} \cdot 11} (3 \sqrt{28})$

$- 2 \sqrt{2^{2} \cdot 11} (3 \sqrt{28})$

Step 2

Pull terms out from under the radical.

$- 2 (2 \sqrt{11}) (3 \sqrt{28})$

Step 3

Multiply $2$ by $- 2$ .

$- 4 \sqrt{11} (3 \sqrt{28})$

Step 4

Rewrite $28$ as $2^{2} \cdot 7$ .

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Step 4.1

Factor $4$ out of $28$ .

$- 4 \sqrt{11} (3 \sqrt{4 (7)})$

Step 4.2

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

$- 4 \sqrt{11} (3 \sqrt{2^{2} \cdot 7})$

$- 4 \sqrt{11} (3 \sqrt{2^{2} \cdot 7})$

Step 5

Pull terms out from under the radical.

$- 4 \sqrt{11} (3 (2 \sqrt{7}))$

Step 6

Multiply $2$ by $3$ .

$- 4 \sqrt{11} (6 \sqrt{7})$

Step 7

Multiply $- 4 \sqrt{11} (6 \sqrt{7})$ .

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Step 7.1

Multiply $6$ by $- 4$ .

$- 24 \sqrt{11} \sqrt{7}$

Step 7.2

Combine using the product rule for radicals.

$- 24 \sqrt{7 \cdot 11}$

Step 7.3

Multiply $7$ by $11$ .

$- 24 \sqrt{77}$

$- 24 \sqrt{77}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- 24 \sqrt{77}$

Decimal Form:

$- 210.59914529 \dots$

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