Basic Math Examples

$4 \sqrt{27} - 3 \sqrt{20}$

Step 1

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 1.1

Factor $9$ out of $27$ .

$4 \sqrt{9 (3)} - 3 \sqrt{20}$

Step 1.2

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

$4 \sqrt{3^{2} \cdot 3} - 3 \sqrt{20}$

$4 \sqrt{3^{2} \cdot 3} - 3 \sqrt{20}$

Step 2

Pull terms out from under the radical.

$4 (3 \sqrt{3}) - 3 \sqrt{20}$

Step 3

Multiply $3$ by $4$ .

$12 \sqrt{3} - 3 \sqrt{20}$

Step 4

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

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Step 4.1

Factor $4$ out of $20$ .

$12 \sqrt{3} - 3 \sqrt{4 (5)}$

Step 4.2

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

$12 \sqrt{3} - 3 \sqrt{2^{2} \cdot 5}$

$12 \sqrt{3} - 3 \sqrt{2^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

$12 \sqrt{3} - 3 (2 \sqrt{5})$

Step 6

Multiply $2$ by $- 3$ .

$12 \sqrt{3} - 6 \sqrt{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt{3} - 6 \sqrt{5}$

Decimal Form:

$7.36820182 \dots$

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