Basic Math Examples

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

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 $63$ .

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

Step 1.1.2

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

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

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

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Step 1.3.1

Factor $4$ out of $28$ .

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

Step 1.3.2

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

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

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

Step 1.4

Pull terms out from under the radical.

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

Step 1.5

Multiply $2$ by $5$ .

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

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

Step 2

Add $3 \sqrt{7}$ and $10 \sqrt{7}$ .

$13 \sqrt{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$13 \sqrt{7}$

Decimal Form:

$34.39476704 \dots$

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