Basic Math Examples

$3 \sqrt{5} + \sqrt{20} - \sqrt{125}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 1.1.1

Factor $4$ out of $20$ .

$3 \sqrt{5} + \sqrt{4 (5)} - \sqrt{125}$

Step 1.1.2

Rewrite $4$ as $2^{2}$ .

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

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

Step 1.2

Pull terms out from under the radical.

$3 \sqrt{5} + 2 \sqrt{5} - \sqrt{125}$

Step 1.3

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

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Step 1.3.1

Factor $25$ out of $125$ .

$3 \sqrt{5} + 2 \sqrt{5} - \sqrt{25 (5)}$

Step 1.3.2

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

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

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

Step 1.4

Pull terms out from under the radical.

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

Step 1.5

Multiply $5$ by $- 1$ .

$3 \sqrt{5} + 2 \sqrt{5} - 5 \sqrt{5}$

$3 \sqrt{5} + 2 \sqrt{5} - 5 \sqrt{5}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $3 \sqrt{5}$ and $2 \sqrt{5}$ .

$5 \sqrt{5} - 5 \sqrt{5}$

Step 2.2

Subtract $5 \sqrt{5}$ from $5 \sqrt{5}$ .

$0$

$0$

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