Pre-Algebra Examples

$\frac{- 42 + \sqrt{1972}}{8}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $1972$ as $2^{2} \cdot 493$ .

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Step 1.1.1

Factor $4$ out of $1972$ .

$\frac{- 42 + \sqrt{4 (493)}}{8}$

Step 1.1.2

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

$\frac{- 42 + \sqrt{2^{2} \cdot 493}}{8}$

Step 1.2

Pull terms out from under the radical.

$\frac{- 42 + 2 \sqrt{493}}{8}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $- 42 + 2 \sqrt{493}$ and $8$ .

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Step 2.1.1

Factor $2$ out of $- 42$ .

$\frac{2 \cdot - 21 + 2 \sqrt{493}}{8}$

Step 2.1.2

Factor $2$ out of $2 \sqrt{493}$ .

$\frac{2 \cdot - 21 + 2 (\sqrt{493})}{8}$

Step 2.1.3

Factor $2$ out of $2 \cdot - 21 + 2 (\sqrt{493})$ .

$\frac{2 \cdot (- 21 + \sqrt{493})}{8}$

Step 2.1.4

Cancel the common factors.

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Step 2.1.4.1

Factor $2$ out of $8$ .

$\frac{2 \cdot (- 21 + \sqrt{493})}{2 (4)}$

Step 2.1.4.2

Cancel the common factor.

$\frac{2 \cdot (- 21 + \sqrt{493})}{2 \cdot 4}$

Step 2.1.4.3

Rewrite the expression.

$\frac{- 21 + \sqrt{493}}{4}$

Step 2.2

Rewrite $- 21$ as $- 1 (21)$ .

$\frac{- 1 (21) + \sqrt{493}}{4}$

Step 2.3

Factor $- 1$ out of $\sqrt{493}$ .

$\frac{- 1 (21) - 1 (- \sqrt{493})}{4}$

Step 2.4

Factor $- 1$ out of $- 1 (21) - 1 (- \sqrt{493})$ .

$\frac{- 1 (21 - \sqrt{493})}{4}$

Step 2.5

Move the negative in front of the fraction.

$- \frac{21 - \sqrt{493}}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{21 - \sqrt{493}}{4}$

Decimal Form:

$0.30090082 \dots$