Basic Math Examples

$5 \sqrt{18} - 2 \sqrt{75}$

Step 1

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

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Step 1.1

Factor $9$ out of $18$ .

$5 \sqrt{9 (2)} - 2 \sqrt{75}$

Step 1.2

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

$5 \sqrt{3^{2} \cdot 2} - 2 \sqrt{75}$

$5 \sqrt{3^{2} \cdot 2} - 2 \sqrt{75}$

Step 2

Pull terms out from under the radical.

$5 (3 \sqrt{2}) - 2 \sqrt{75}$

Step 3

Multiply $3$ by $5$ .

$15 \sqrt{2} - 2 \sqrt{75}$

Step 4

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 4.1

Factor $25$ out of $75$ .

$15 \sqrt{2} - 2 \sqrt{25 (3)}$

Step 4.2

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

$15 \sqrt{2} - 2 \sqrt{5^{2} \cdot 3}$

$15 \sqrt{2} - 2 \sqrt{5^{2} \cdot 3}$

Step 5

Pull terms out from under the radical.

$15 \sqrt{2} - 2 (5 \sqrt{3})$

Step 6

Multiply $5$ by $- 2$ .

$15 \sqrt{2} - 10 \sqrt{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$15 \sqrt{2} - 10 \sqrt{3}$

Decimal Form:

$3.89269535 \dots$

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