Pre-Algebra Examples

$3 \sqrt{8} - \sqrt{125} + \sqrt{32} + \sqrt{45}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $8$ .

$3 \sqrt{4 (2)} - \sqrt{125} + \sqrt{32} + \sqrt{45}$

Step 1.1.2

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

$3 \sqrt{2^{2} \cdot 2} - \sqrt{125} + \sqrt{32} + \sqrt{45}$

Step 1.2

Pull terms out from under the radical.

$3 (2 \sqrt{2}) - \sqrt{125} + \sqrt{32} + \sqrt{45}$

Step 1.3

Multiply $2$ by $3$ .

$6 \sqrt{2} - \sqrt{125} + \sqrt{32} + \sqrt{45}$

Step 1.4

Rewrite $125$ as $5^{2} \cdot 5$ .

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Step 1.4.1

Factor $25$ out of $125$ .

$6 \sqrt{2} - \sqrt{25 (5)} + \sqrt{32} + \sqrt{45}$

Step 1.4.2

Rewrite $25$ as $5^{2}$ .

$6 \sqrt{2} - \sqrt{5^{2} \cdot 5} + \sqrt{32} + \sqrt{45}$

Step 1.5

Pull terms out from under the radical.

$6 \sqrt{2} - (5 \sqrt{5}) + \sqrt{32} + \sqrt{45}$

Step 1.6

Multiply $5$ by $- 1$ .

$6 \sqrt{2} - 5 \sqrt{5} + \sqrt{32} + \sqrt{45}$

Step 1.7

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 1.7.1

Factor $16$ out of $32$ .

$6 \sqrt{2} - 5 \sqrt{5} + \sqrt{16 (2)} + \sqrt{45}$

Step 1.7.2

Rewrite $16$ as $4^{2}$ .

$6 \sqrt{2} - 5 \sqrt{5} + \sqrt{4^{2} \cdot 2} + \sqrt{45}$

Step 1.8

Pull terms out from under the radical.

$6 \sqrt{2} - 5 \sqrt{5} + 4 \sqrt{2} + \sqrt{45}$

Step 1.9

Rewrite $45$ as $3^{2} \cdot 5$ .

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Step 1.9.1

Factor $9$ out of $45$ .

$6 \sqrt{2} - 5 \sqrt{5} + 4 \sqrt{2} + \sqrt{9 (5)}$

Step 1.9.2

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

$6 \sqrt{2} - 5 \sqrt{5} + 4 \sqrt{2} + \sqrt{3^{2} \cdot 5}$

Step 1.10

Pull terms out from under the radical.

$6 \sqrt{2} - 5 \sqrt{5} + 4 \sqrt{2} + 3 \sqrt{5}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $6 \sqrt{2}$ and $4 \sqrt{2}$ .

$10 \sqrt{2} - 5 \sqrt{5} + 3 \sqrt{5}$

Step 2.2

Add $- 5 \sqrt{5}$ and $3 \sqrt{5}$ .

$10 \sqrt{2} - 2 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{2} - 2 \sqrt{5}$

Decimal Form:

$9.66999966 \dots$