Basic Math Examples

arctan (\sqrt{1250 \div 8})

$\arctan (\sqrt{1250 \div 8})$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Rewrite the division as a fraction.

arctan (\sqrt{\frac{1250}{8}})

$\arctan (\sqrt{\frac{1250}{8}})$

Step 1.2

Cancel the common factor of

1250

$1250$ and

8

$8$ .

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Step 1.2.1

Factor

2

$2$ out of

1250

$1250$ .

arctan ⎛ ⎝ \sqrt{\frac{2 (625)}{8}} ⎞ ⎠

$\arctan (\sqrt{\frac{2 (625)}{8}})$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor

2

$2$ out of

8

$8$ .

arctan (\sqrt{\frac{2 \cdot 625}{2 \cdot 4}})

$\arctan (\sqrt{\frac{2 \cdot 625}{2 \cdot 4}})$

Step 1.2.2.2

Cancel the common factor.

$\arctan (\sqrt{\frac{2 \cdot 625}{2 \cdot 4}})$

Step 1.2.2.3

Rewrite the expression.

$\arctan (\sqrt{\frac{625}{4}})$

Step 2

Rewrite

$\sqrt{\frac{625}{4}}$ as

$\frac{\sqrt{625}}{\sqrt{4}}$ .

$\arctan (\frac{\sqrt{625}}{\sqrt{4}})$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite

$625$ as

$25^{2}$ .

$\arctan (\frac{\sqrt{25^{2}}}{\sqrt{4}})$

Step 3.2

Pull terms out from under the radical, assuming positive real numbers.

$\arctan (\frac{25}{\sqrt{4}})$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite

$4$ as

$2^{2}$ .

$\arctan (\frac{25}{\sqrt{2^{2}}})$

Step 4.2

Pull terms out from under the radical, assuming positive real numbers.

$\arctan (\frac{25}{2})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\arctan (\frac{25}{2})$

Decimal Form:

$1.49096634 \dots$