Basic Math Examples

\sqrt{63} + 5 \sqrt{28}

$\sqrt{63} + 5 \sqrt{28}$

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

$63$ .

\sqrt{9 (7)} + 5 \sqrt{28}

$\sqrt{9 (7)} + 5 \sqrt{28}$

Step 1.1.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

\sqrt{3^{2} \cdot 7} + 5 \sqrt{28}

$\sqrt{3^{2} \cdot 7} + 5 \sqrt{28}$

\sqrt{3^{2} \cdot 7} + 5 \sqrt{28}

$\sqrt{3^{2} \cdot 7} + 5 \sqrt{28}$

Step 1.2

Pull terms out from under the radical.

3 \sqrt{7} + 5 \sqrt{28}

$3 \sqrt{7} + 5 \sqrt{28}$

Step 1.3

Rewrite

28

$28$ as

2^{2} \cdot 7

$2^{2} \cdot 7$ .

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Step 1.3.1

Factor

4

$4$ out of

28

$28$ .

3 \sqrt{7} + 5 \sqrt{4 (7)}

$3 \sqrt{7} + 5 \sqrt{4 (7)}$

Step 1.3.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

3 \sqrt{7} + 5 \sqrt{2^{2} \cdot 7}

$3 \sqrt{7} + 5 \sqrt{2^{2} \cdot 7}$

3 \sqrt{7} + 5 \sqrt{2^{2} \cdot 7}

$3 \sqrt{7} + 5 \sqrt{2^{2} \cdot 7}$

Step 1.4

Pull terms out from under the radical.

3 \sqrt{7} + 5 (2 \sqrt{7})

$3 \sqrt{7} + 5 (2 \sqrt{7})$

Step 1.5

Multiply

2

$2$ by

5

$5$ .

3 \sqrt{7} + 10 \sqrt{7}

$3 \sqrt{7} + 10 \sqrt{7}$

3 \sqrt{7} + 10 \sqrt{7}

$3 \sqrt{7} + 10 \sqrt{7}$

Step 2

Add

3 \sqrt{7}

$3 \sqrt{7}$ and

10 \sqrt{7}

$10 \sqrt{7}$ .

$13 \sqrt{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$13 \sqrt{7}$

Decimal Form:

$34.39476704 \dots$

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