Algebra Examples

\sqrt{45}

$\sqrt{45}$

Step 1

Rewrite

45

$45$ as

3^{2} \cdot 5

$3^{2} \cdot 5$ .

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Step 1.1

Factor

9

$9$ out of

45

$45$ .

\sqrt{9 (5)}

$\sqrt{9 (5)}$

Step 1.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

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

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

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

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

Step 2

Pull terms out from under the radical.

3 \sqrt{5}

$3 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

3 \sqrt{5}

$3 \sqrt{5}$

Decimal Form:

6.70820393 \dots

$6.70820393 \dots$

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

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