Basic Math Examples

$3 \sqrt{20} - \sqrt{45} + 4 \sqrt{80}$

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 $20$ .

$3 \sqrt{4 (5)} - \sqrt{45} + 4 \sqrt{80}$

Step 1.1.2

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

$3 \sqrt{2^{2} \cdot 5} - \sqrt{45} + 4 \sqrt{80}$

$3 \sqrt{2^{2} \cdot 5} - \sqrt{45} + 4 \sqrt{80}$

Step 1.2

Pull terms out from under the radical.

$3 (2 \sqrt{5}) - \sqrt{45} + 4 \sqrt{80}$

Step 1.3

Multiply $2$ by $3$ .

$6 \sqrt{5} - \sqrt{45} + 4 \sqrt{80}$

Step 1.4

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

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Step 1.4.1

Factor $9$ out of $45$ .

$6 \sqrt{5} - \sqrt{9 (5)} + 4 \sqrt{80}$

Step 1.4.2

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

$6 \sqrt{5} - \sqrt{3^{2} \cdot 5} + 4 \sqrt{80}$

$6 \sqrt{5} - \sqrt{3^{2} \cdot 5} + 4 \sqrt{80}$

Step 1.5

Pull terms out from under the radical.

$6 \sqrt{5} - (3 \sqrt{5}) + 4 \sqrt{80}$

Step 1.6

Multiply $3$ by $- 1$ .

$6 \sqrt{5} - 3 \sqrt{5} + 4 \sqrt{80}$

Step 1.7

Rewrite $80$ as $4^{2} \cdot 5$ .

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Step 1.7.1

Factor $16$ out of $80$ .

$6 \sqrt{5} - 3 \sqrt{5} + 4 \sqrt{16 (5)}$

Step 1.7.2

Rewrite $16$ as $4^{2}$ .

$6 \sqrt{5} - 3 \sqrt{5} + 4 \sqrt{4^{2} \cdot 5}$

$6 \sqrt{5} - 3 \sqrt{5} + 4 \sqrt{4^{2} \cdot 5}$

Step 1.8

Pull terms out from under the radical.

$6 \sqrt{5} - 3 \sqrt{5} + 4 (4 \sqrt{5})$

Step 1.9

Multiply $4$ by $4$ .

$6 \sqrt{5} - 3 \sqrt{5} + 16 \sqrt{5}$

$6 \sqrt{5} - 3 \sqrt{5} + 16 \sqrt{5}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $3 \sqrt{5}$ from $6 \sqrt{5}$ .

$3 \sqrt{5} + 16 \sqrt{5}$

Step 2.2

Add $3 \sqrt{5}$ and $16 \sqrt{5}$ .

$19 \sqrt{5}$

$19 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$19 \sqrt{5}$

Decimal Form:

$42.48529157 \dots$

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