Basic Math Examples

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

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

Step 1

Simplify each term.

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Step 1.1

Rewrite

63

$63$ as

3^{2} \cdot 7

$3^{2} \cdot 7$ .

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Step 1.1.1

Factor

9

$9$ out of

63

$63$ .

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

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

Step 1.1.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

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

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

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}

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

Step 1.3

Multiply

3

$3$ by

4

$4$ .

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

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

Step 1.4

Rewrite

28

$28$ as

2^{2} \cdot 7

$2^{2} \cdot 7$ .

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Step 1.4.1

Factor

4

$4$ out of

28

$28$ .

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

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

Step 1.4.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

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})

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

Step 1.6

Multiply

2

$2$ by

- 1

$- 1$ .

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

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

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}

$12 \sqrt{7}$ and

2 \sqrt{7}

$2 \sqrt{7}$ .

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

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

Step 2.2

Subtract

2 \sqrt{7}

$2 \sqrt{7}$ from

14 \sqrt{7}

$14 \sqrt{7}$ .

12 \sqrt{7}

$12 \sqrt{7}$

12 \sqrt{7}

$12 \sqrt{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

12 \sqrt{7}

$12 \sqrt{7}$

Decimal Form:

31.74901573 \dots

$31.74901573 \dots$

Enter a problem...

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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