Basic Math Examples

$(5 + \sqrt{2}) - (8 + \sqrt{18})$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

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

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Step 1.1.1.1

Factor $9$ out of $18$ .

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

Step 1.1.1.2

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

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

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

Step 1.1.2

Pull terms out from under the radical.

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

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

Step 1.2

Apply the distributive property.

$5 + \sqrt{2} - 1 \cdot 8 - (3 \sqrt{2})$

Step 1.3

Multiply $- 1$ by $8$ .

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

Step 1.4

Multiply $3$ by $- 1$ .

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

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

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $8$ from $5$ .

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

Step 2.2

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

$- 3 - 2 \sqrt{2}$

$- 3 - 2 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 3 - 2 \sqrt{2}$

Decimal Form:

$- 5.82842712 \dots$

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