Basic Math Examples

\sqrt{45} - \sqrt{320}

$\sqrt{45} - \sqrt{320}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

45

$45$ as

3^{2} \cdot 5

$3^{2} \cdot 5$ .

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Step 1.1.1

Factor

9

$9$ out of

45

$45$ .

\sqrt{9 (5)} - \sqrt{320}

$\sqrt{9 (5)} - \sqrt{320}$

Step 1.1.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

\sqrt{3^{2} \cdot 5} - \sqrt{320}

$\sqrt{3^{2} \cdot 5} - \sqrt{320}$

\sqrt{3^{2} \cdot 5} - \sqrt{320}

$\sqrt{3^{2} \cdot 5} - \sqrt{320}$

Step 1.2

Pull terms out from under the radical.

3 \sqrt{5} - \sqrt{320}

$3 \sqrt{5} - \sqrt{320}$

Step 1.3

Rewrite

320

$320$ as

8^{2} \cdot 5

$8^{2} \cdot 5$ .

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Step 1.3.1

Factor

64

$64$ out of

320

$320$ .

3 \sqrt{5} - \sqrt{64 (5)}

$3 \sqrt{5} - \sqrt{64 (5)}$

Step 1.3.2

Rewrite

64

$64$ as

8^{2}

$8^{2}$ .

3 \sqrt{5} - \sqrt{8^{2} \cdot 5}

$3 \sqrt{5} - \sqrt{8^{2} \cdot 5}$

3 \sqrt{5} - \sqrt{8^{2} \cdot 5}

$3 \sqrt{5} - \sqrt{8^{2} \cdot 5}$

Step 1.4

Pull terms out from under the radical.

3 \sqrt{5} - (8 \sqrt{5})

$3 \sqrt{5} - (8 \sqrt{5})$

Step 1.5

Multiply

8

$8$ by

- 1

$- 1$ .

3 \sqrt{5} - 8 \sqrt{5}

$3 \sqrt{5} - 8 \sqrt{5}$

3 \sqrt{5} - 8 \sqrt{5}

$3 \sqrt{5} - 8 \sqrt{5}$

Step 2

Subtract

8 \sqrt{5}

$8 \sqrt{5}$ from

3 \sqrt{5}

$3 \sqrt{5}$ .

- 5 \sqrt{5}

$- 5 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

- 5 \sqrt{5}

$- 5 \sqrt{5}$

Decimal Form:

- 11.18033988 \dots

$- 11.18033988 \dots$

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

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