Basic Math Examples

$\sqrt{28} + \sqrt{32} - 2 \sqrt{2}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $28$ .

$\sqrt{4 (7)} + \sqrt{32} - 2 \sqrt{2}$

Step 1.1.2

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

$\sqrt{2^{2} \cdot 7} + \sqrt{32} - 2 \sqrt{2}$

$\sqrt{2^{2} \cdot 7} + \sqrt{32} - 2 \sqrt{2}$

Step 1.2

Pull terms out from under the radical.

$2 \sqrt{7} + \sqrt{32} - 2 \sqrt{2}$

Step 1.3

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 1.3.1

Factor $16$ out of $32$ .

$2 \sqrt{7} + \sqrt{16 (2)} - 2 \sqrt{2}$

Step 1.3.2

Rewrite $16$ as $4^{2}$ .

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

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

Step 1.4

Pull terms out from under the radical.

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

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

Step 2

Subtract $2 \sqrt{2}$ from $4 \sqrt{2}$ .

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$8.11992974 \dots$

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