Pre-Algebra Examples

$\sqrt{5} + \sqrt{45} + \sqrt{125}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $45$ as $3^{2} \cdot 5$ .

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Step 1.1.1

Factor $9$ out of $45$ .

$\sqrt{5} + \sqrt{9 (5)} + \sqrt{125}$

Step 1.1.2

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

$\sqrt{5} + \sqrt{3^{2} \cdot 5} + \sqrt{125}$

$\sqrt{5} + \sqrt{3^{2} \cdot 5} + \sqrt{125}$

Step 1.2

Pull terms out from under the radical.

$\sqrt{5} + 3 \sqrt{5} + \sqrt{125}$

Step 1.3

Rewrite $125$ as $5^{2} \cdot 5$ .

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Step 1.3.1

Factor $25$ out of $125$ .

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

Step 1.3.2

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

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

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

Step 1.4

Pull terms out from under the radical.

$\sqrt{5} + 3 \sqrt{5} + 5 \sqrt{5}$

$\sqrt{5} + 3 \sqrt{5} + 5 \sqrt{5}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $\sqrt{5}$ and $3 \sqrt{5}$ .

$4 \sqrt{5} + 5 \sqrt{5}$

Step 2.2

Add $4 \sqrt{5}$ and $5 \sqrt{5}$ .

$9 \sqrt{5}$

$9 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$9 \sqrt{5}$

Decimal Form:

$20.12461179 \dots$

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