Basic Math Examples

\sqrt{80} - \sqrt{180}

$\sqrt{80} - \sqrt{180}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

80

$80$ as

4^{2} \cdot 5

$4^{2} \cdot 5$ .

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Step 1.1.1

Factor

16

$16$ out of

80

$80$ .

\sqrt{16 (5)} - \sqrt{180}

$\sqrt{16 (5)} - \sqrt{180}$

Step 1.1.2

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

\sqrt{4^{2} \cdot 5} - \sqrt{180}

$\sqrt{4^{2} \cdot 5} - \sqrt{180}$

\sqrt{4^{2} \cdot 5} - \sqrt{180}

$\sqrt{4^{2} \cdot 5} - \sqrt{180}$

Step 1.2

Pull terms out from under the radical.

4 \sqrt{5} - \sqrt{180}

$4 \sqrt{5} - \sqrt{180}$

Step 1.3

Rewrite

180

$180$ as

6^{2} \cdot 5

$6^{2} \cdot 5$ .

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Step 1.3.1

Factor

36

$36$ out of

180

$180$ .

4 \sqrt{5} - \sqrt{36 (5)}

$4 \sqrt{5} - \sqrt{36 (5)}$

Step 1.3.2

Rewrite

36

$36$ as

6^{2}

$6^{2}$ .

4 \sqrt{5} - \sqrt{6^{2} \cdot 5}

$4 \sqrt{5} - \sqrt{6^{2} \cdot 5}$

4 \sqrt{5} - \sqrt{6^{2} \cdot 5}

$4 \sqrt{5} - \sqrt{6^{2} \cdot 5}$

Step 1.4

Pull terms out from under the radical.

4 \sqrt{5} - (6 \sqrt{5})

$4 \sqrt{5} - (6 \sqrt{5})$

Step 1.5

Multiply

6

$6$ by

- 1

$- 1$ .

4 \sqrt{5} - 6 \sqrt{5}

$4 \sqrt{5} - 6 \sqrt{5}$

4 \sqrt{5} - 6 \sqrt{5}

$4 \sqrt{5} - 6 \sqrt{5}$

Step 2

Subtract

6 \sqrt{5}

$6 \sqrt{5}$ from

4 \sqrt{5}

$4 \sqrt{5}$ .

- 2 \sqrt{5}

$- 2 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

- 2 \sqrt{5}

$- 2 \sqrt{5}$

Decimal Form:

- 4.47213595 \dots

$- 4.47213595 \dots$

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

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