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Precalculus Examples

\sqrt{27}

$\sqrt{27}$

Step 1

Rewrite

27

$27$ as

3^{2} \cdot 3

$3^{2} \cdot 3$ .

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Step 1.1

Factor

9

$9$ out of

27

$27$ .

\sqrt{9 (3)}

$\sqrt{9 (3)}$

Step 1.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

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

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

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

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

Step 2

Pull terms out from under the radical.

3 \sqrt{3}

$3 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

3 \sqrt{3}

$3 \sqrt{3}$

Decimal Form:

5.19615242 \dots

$5.19615242 \dots$

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

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