Pre-Algebra Examples

$2 \sqrt{28} + 2 \sqrt{8} - 5 \sqrt{27}$

Step 1

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

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Step 1.1

Factor $4$ out of $28$ .

$2 \sqrt{4 (7)} + 2 \sqrt{8} - 5 \sqrt{27}$

Step 1.2

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

$2 \sqrt{2^{2} \cdot 7} + 2 \sqrt{8} - 5 \sqrt{27}$

Step 2

Pull terms out from under the radical.

$2 (2 \sqrt{7}) + 2 \sqrt{8} - 5 \sqrt{27}$

Step 3

Multiply $2$ by $2$ .

$4 \sqrt{7} + 2 \sqrt{8} - 5 \sqrt{27}$

Step 4

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 4.1

Factor $4$ out of $8$ .

$4 \sqrt{7} + 2 \sqrt{4 (2)} - 5 \sqrt{27}$

Step 4.2

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

$4 \sqrt{7} + 2 \sqrt{2^{2} \cdot 2} - 5 \sqrt{27}$

Step 5

Pull terms out from under the radical.

$4 \sqrt{7} + 2 (2 \sqrt{2}) - 5 \sqrt{27}$

Step 6

Multiply $2$ by $2$ .

$4 \sqrt{7} + 4 \sqrt{2} - 5 \sqrt{27}$

Step 7

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 7.1

Factor $9$ out of $27$ .

$4 \sqrt{7} + 4 \sqrt{2} - 5 \sqrt{9 (3)}$

Step 7.2

Rewrite $9$ as $3^{2}$ .

$4 \sqrt{7} + 4 \sqrt{2} - 5 \sqrt{3^{2} \cdot 3}$

Step 8

Pull terms out from under the radical.

$4 \sqrt{7} + 4 \sqrt{2} - 5 (3 \sqrt{3})$

Step 9

Multiply $3$ by $- 5$ .

$4 \sqrt{7} + 4 \sqrt{2} - 15 \sqrt{3}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{7} + 4 \sqrt{2} - 15 \sqrt{3}$

Decimal Form:

$- 9.74090261 \dots$