Basic Math Examples

$4 \sqrt{45} + \sqrt{20}$

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 $45$ .

$4 \sqrt{9 (5)} + \sqrt{20}$

Step 1.1.2

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

$4 \sqrt{3^{2} \cdot 5} + \sqrt{20}$

$4 \sqrt{3^{2} \cdot 5} + \sqrt{20}$

Step 1.2

Pull terms out from under the radical.

$4 (3 \sqrt{5}) + \sqrt{20}$

Step 1.3

Multiply $3$ by $4$ .

$12 \sqrt{5} + \sqrt{20}$

Step 1.4

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

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Step 1.4.1

Factor $4$ out of $20$ .

$12 \sqrt{5} + \sqrt{4 (5)}$

Step 1.4.2

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

$12 \sqrt{5} + \sqrt{2^{2} \cdot 5}$

$12 \sqrt{5} + \sqrt{2^{2} \cdot 5}$

Step 1.5

Pull terms out from under the radical.

$12 \sqrt{5} + 2 \sqrt{5}$

$12 \sqrt{5} + 2 \sqrt{5}$

Step 2

Add $12 \sqrt{5}$ and $2 \sqrt{5}$ .

$14 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$14 \sqrt{5}$

Decimal Form:

$31.30495168 \dots$

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