Pre-Algebra Examples

$2 \sqrt{27} + 8 \sqrt{3} + 5 \sqrt{8}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $9$ out of $27$ .

$2 \sqrt{9 (3)} + 8 \sqrt{3} + 5 \sqrt{8}$

Step 1.1.2

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

$2 \sqrt{3^{2} \cdot 3} + 8 \sqrt{3} + 5 \sqrt{8}$

Step 1.2

Pull terms out from under the radical.

$2 (3 \sqrt{3}) + 8 \sqrt{3} + 5 \sqrt{8}$

Step 1.3

Multiply $3$ by $2$ .

$6 \sqrt{3} + 8 \sqrt{3} + 5 \sqrt{8}$

Step 1.4

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

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Step 1.4.1

Factor $4$ out of $8$ .

$6 \sqrt{3} + 8 \sqrt{3} + 5 \sqrt{4 (2)}$

Step 1.4.2

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

$6 \sqrt{3} + 8 \sqrt{3} + 5 \sqrt{2^{2} \cdot 2}$

Step 1.5

Pull terms out from under the radical.

$6 \sqrt{3} + 8 \sqrt{3} + 5 (2 \sqrt{2})$

Step 1.6

Multiply $2$ by $5$ .

$6 \sqrt{3} + 8 \sqrt{3} + 10 \sqrt{2}$

Step 2

Add $6 \sqrt{3}$ and $8 \sqrt{3}$ .

$14 \sqrt{3} + 10 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$14 \sqrt{3} + 10 \sqrt{2}$

Decimal Form:

$38.39084692 \dots$