Pre-Algebra Examples

$\sqrt{112} + \sqrt{32} - \sqrt{80}$

Step 1

Rewrite $112$ as $4^{2} \cdot 7$ .

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Step 1.1

Factor $16$ out of $112$ .

$\sqrt{16 (7)} + \sqrt{32} - \sqrt{80}$

Step 1.2

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

$\sqrt{4^{2} \cdot 7} + \sqrt{32} - \sqrt{80}$

$\sqrt{4^{2} \cdot 7} + \sqrt{32} - \sqrt{80}$

Step 2

Pull terms out from under the radical.

$4 \sqrt{7} + \sqrt{32} - \sqrt{80}$

Step 3

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

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Step 3.1

Factor $16$ out of $32$ .

$4 \sqrt{7} + \sqrt{16 (2)} - \sqrt{80}$

Step 3.2

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

$4 \sqrt{7} + \sqrt{4^{2} \cdot 2} - \sqrt{80}$

$4 \sqrt{7} + \sqrt{4^{2} \cdot 2} - \sqrt{80}$

Step 4

Pull terms out from under the radical.

$4 \sqrt{7} + 4 \sqrt{2} - \sqrt{80}$

Step 5

Rewrite $80$ as $4^{2} \cdot 5$ .

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Step 5.1

Factor $16$ out of $80$ .

$4 \sqrt{7} + 4 \sqrt{2} - \sqrt{16 (5)}$

Step 5.2

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

$4 \sqrt{7} + 4 \sqrt{2} - \sqrt{4^{2} \cdot 5}$

$4 \sqrt{7} + 4 \sqrt{2} - \sqrt{4^{2} \cdot 5}$

Step 6

Pull terms out from under the radical.

$4 \sqrt{7} + 4 \sqrt{2} - (4 \sqrt{5})$

Step 7

Multiply $4$ by $- 1$ .

$4 \sqrt{7} + 4 \sqrt{2} - 4 \sqrt{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{7} + 4 \sqrt{2} - 4 \sqrt{5}$

Decimal Form:

$7.29558758 \dots$

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