Algebra Examples

$\frac{4 + \sqrt{121} - 2 \cdot 3^{3}}{| - 19 - 2 \cdot - 8 |}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $121$ as $11^{2}$ .

$\frac{4 + \sqrt{11^{2}} - 2 \cdot 3^{3}}{| - 19 - 2 \cdot - 8 |}$

Step 1.2

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

$\frac{4 + 11 - 2 \cdot 3^{3}}{| - 19 - 2 \cdot - 8 |}$

Step 1.3

Raise $3$ to the power of $3$ .

$\frac{4 + 11 - 2 \cdot 27}{| - 19 - 2 \cdot - 8 |}$

Step 1.4

Multiply $- 2$ by $27$ .

$\frac{4 + 11 - 54}{| - 19 - 2 \cdot - 8 |}$

Step 1.5

Add $4$ and $11$ .

$\frac{15 - 54}{| - 19 - 2 \cdot - 8 |}$

Step 1.6

Subtract $54$ from $15$ .

$\frac{- 39}{| - 19 - 2 \cdot - 8 |}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $- 2$ by $- 8$ .

$\frac{- 39}{| - 19 + 16 |}$

Step 2.2

Add $- 19$ and $16$ .

$\frac{- 39}{| - 3 |}$

Step 2.3

The absolute value is the distance between a number and zero. The distance between $- 3$ and $0$ is $3$ .

$\frac{- 39}{3}$

Step 3

Divide $- 39$ by $3$ .

$- 13$