Pre-Algebra Examples

$- 16 + \sqrt{57000} \div 16$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$- 16 + \frac{\sqrt{57000}}{16}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

Rewrite $57000$ as $10^{2} \cdot 570$ .

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Step 1.2.1.1

Factor $100$ out of $57000$ .

$- 16 + \frac{\sqrt{100 (570)}}{16}$

Step 1.2.1.2

Rewrite $100$ as $10^{2}$ .

$- 16 + \frac{\sqrt{10^{2} \cdot 570}}{16}$

Step 1.2.2

Pull terms out from under the radical.

$- 16 + \frac{10 \sqrt{570}}{16}$

Step 1.3

Cancel the common factor of $10$ and $16$ .

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Step 1.3.1

Factor $2$ out of $10 \sqrt{570}$ .

$- 16 + \frac{2 (5 \sqrt{570})}{16}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $2$ out of $16$ .

$- 16 + \frac{2 (5 \sqrt{570})}{2 (8)}$

Step 1.3.2.2

Cancel the common factor.

$- 16 + \frac{2 (5 \sqrt{570})}{2 \cdot 8}$

Step 1.3.2.3

Rewrite the expression.

$- 16 + \frac{5 \sqrt{570}}{8}$

Step 2

To write $- 16$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- 16 \cdot \frac{8}{8} + \frac{5 \sqrt{570}}{8}$

Step 3

Combine $- 16$ and $\frac{8}{8}$ .

$\frac{- 16 \cdot 8}{8} + \frac{5 \sqrt{570}}{8}$

Step 4

Simplify the expression.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{- 16 \cdot 8 + 5 \sqrt{570}}{8}$

Step 4.2

Multiply $- 16$ by $8$ .

$\frac{- 128 + 5 \sqrt{570}}{8}$

Step 5

Rewrite $- 128$ as $- 1 (128)$ .

$\frac{- 1 (128) + 5 \sqrt{570}}{8}$

Step 6

Factor $- 1$ out of $5 \sqrt{570}$ .

$\frac{- 1 (128) - (- 5 \sqrt{570})}{8}$

Step 7

Factor $- 1$ out of $- 1 (128) - (- 5 \sqrt{570})$ .

$\frac{- 1 (128 - 5 \sqrt{570})}{8}$

Step 8

Move the negative in front of the fraction.

$- \frac{128 - 5 \sqrt{570}}{8}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{128 - 5 \sqrt{570}}{8}$

Decimal Form:

$- 1.07832951 \dots$