Pre-Algebra Examples

$3 \sqrt{8} + \sqrt{50} - \sqrt{18}$

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 $8$ .

$3 \sqrt{4 (2)} + \sqrt{50} - \sqrt{18}$

Step 1.1.2

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

$3 \sqrt{2^{2} \cdot 2} + \sqrt{50} - \sqrt{18}$

$3 \sqrt{2^{2} \cdot 2} + \sqrt{50} - \sqrt{18}$

Step 1.2

Pull terms out from under the radical.

$3 (2 \sqrt{2}) + \sqrt{50} - \sqrt{18}$

Step 1.3

Multiply $2$ by $3$ .

$6 \sqrt{2} + \sqrt{50} - \sqrt{18}$

Step 1.4

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 1.4.1

Factor $25$ out of $50$ .

$6 \sqrt{2} + \sqrt{25 (2)} - \sqrt{18}$

Step 1.4.2

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

$6 \sqrt{2} + \sqrt{5^{2} \cdot 2} - \sqrt{18}$

$6 \sqrt{2} + \sqrt{5^{2} \cdot 2} - \sqrt{18}$

Step 1.5

Pull terms out from under the radical.

$6 \sqrt{2} + 5 \sqrt{2} - \sqrt{18}$

Step 1.6

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 1.6.1

Factor $9$ out of $18$ .

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

Step 1.6.2

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

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

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

Step 1.7

Pull terms out from under the radical.

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

Step 1.8

Multiply $3$ by $- 1$ .

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

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

Step 2

Simplify by adding terms.

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Step 2.1

Add $6 \sqrt{2}$ and $5 \sqrt{2}$ .

$11 \sqrt{2} - 3 \sqrt{2}$

Step 2.2

Subtract $3 \sqrt{2}$ from $11 \sqrt{2}$ .

$8 \sqrt{2}$

$8 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt{2}$

Decimal Form:

$11.31370849 \dots$

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