Basic Math Examples

5 \cdot \sqrt{75}

$5 \cdot \sqrt{75}$

Step 1

Rewrite

75

$75$ as

5^{2} \cdot 3

$5^{2} \cdot 3$ .

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Step 1.1

Factor

25

$25$ out of

75

$75$ .

5 \cdot \sqrt{25 (3)}

$5 \cdot \sqrt{25 (3)}$

Step 1.2

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

5 \cdot \sqrt{5^{2} \cdot 3}

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

5 \cdot \sqrt{5^{2} \cdot 3}

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

Step 2

Pull terms out from under the radical.

5 \cdot (5 \sqrt{3})

$5 \cdot (5 \sqrt{3})$

Step 3

Multiply

5

$5$ by

5

$5$ .

25 \sqrt{3}

$25 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

25 \sqrt{3}

$25 \sqrt{3}$

Decimal Form:

43.30127018 \dots

$43.30127018 \dots$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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