Basic Math Examples

$4 \sqrt{63} + 2 \sqrt{7} - \sqrt{28}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $63$ as $3^{2} \cdot 7$ .

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Step 1.1.1

Factor $9$ out of $63$ .

$4 \sqrt{9 (7)} + 2 \sqrt{7} - \sqrt{28}$

Step 1.1.2

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

$4 \sqrt{3^{2} \cdot 7} + 2 \sqrt{7} - \sqrt{28}$

$4 \sqrt{3^{2} \cdot 7} + 2 \sqrt{7} - \sqrt{28}$

Step 1.2

Pull terms out from under the radical.

$4 (3 \sqrt{7}) + 2 \sqrt{7} - \sqrt{28}$

Step 1.3

Multiply $3$ by $4$ .

$12 \sqrt{7} + 2 \sqrt{7} - \sqrt{28}$

Step 1.4

Rewrite $28$ as $2^{2} \cdot 7$ .

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Step 1.4.1

Factor $4$ out of $28$ .

$12 \sqrt{7} + 2 \sqrt{7} - \sqrt{4 (7)}$

Step 1.4.2

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

$12 \sqrt{7} + 2 \sqrt{7} - \sqrt{2^{2} \cdot 7}$

$12 \sqrt{7} + 2 \sqrt{7} - \sqrt{2^{2} \cdot 7}$

Step 1.5

Pull terms out from under the radical.

$12 \sqrt{7} + 2 \sqrt{7} - (2 \sqrt{7})$

Step 1.6

Multiply $2$ by $- 1$ .

$12 \sqrt{7} + 2 \sqrt{7} - 2 \sqrt{7}$

$12 \sqrt{7} + 2 \sqrt{7} - 2 \sqrt{7}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $12 \sqrt{7}$ and $2 \sqrt{7}$ .

$14 \sqrt{7} - 2 \sqrt{7}$

Step 2.2

Subtract $2 \sqrt{7}$ from $14 \sqrt{7}$ .

$12 \sqrt{7}$

$12 \sqrt{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt{7}$

Decimal Form:

$31.74901573 \dots$

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