Evaluate (4((3-5)^3-2(5/2)^2)+3(2/6))- square root of 4

$(4 ({(3 - 5)}^{3} - 2 {(\frac{5}{2})}^{2}) + 3 (\frac{2}{6})) - \sqrt{4}$

Step 1

Simplify each term.

Subtract $5$ from $3$ .

$4 ({(- 2)}^{3} - 2 {(\frac{5}{2})}^{2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Raise $- 2$ to the power of $3$ .

$4 (- 8 - 2 {(\frac{5}{2})}^{2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Apply the product rule to $\frac{5}{2}$ .

$4 (- 8 - 2 \frac{5^{2}}{2^{2}}) + 3 (\frac{2}{6}) - \sqrt{4}$

Raise $5$ to the power of $2$ .

$4 (- 8 - 2 \frac{25}{2^{2}}) + 3 (\frac{2}{6}) - \sqrt{4}$

Raise $2$ to the power of $2$ .

$4 (- 8 - 2 (\frac{25}{4})) + 3 (\frac{2}{6}) - \sqrt{4}$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$4 (- 8 + 2 (- 1) \frac{25}{4}) + 3 (\frac{2}{6}) - \sqrt{4}$

Factor $2$ out of $4$ .

$4 (- 8 + 2 \cdot - 1 \frac{25}{2 \cdot 2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Cancel the common factor.

$4 (- 8 + 2 \cdot - 1 \frac{25}{2 \cdot 2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Rewrite the expression.

$4 (- 8 - 1 (\frac{25}{2})) + 3 (\frac{2}{6}) - \sqrt{4}$

Rewrite $- 1 (\frac{25}{2})$ as $- (\frac{25}{2})$ .

$4 (- 8 - \frac{25}{2}) + 3 (\frac{2}{6}) - \sqrt{4}$

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$4 (- 8 \cdot \frac{2}{2} - \frac{25}{2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Combine $- 8$ and $\frac{2}{2}$ .

$4 (\frac{- 8 \cdot 2}{2} - \frac{25}{2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Combine the numerators over the common denominator.

$4 \frac{- 8 \cdot 2 - 25}{2} + 3 (\frac{2}{6}) - \sqrt{4}$

Simplify the numerator.

Multiply $- 8$ by $2$ .

$4 \frac{- 16 - 25}{2} + 3 (\frac{2}{6}) - \sqrt{4}$

Subtract $25$ from $- 16$ .

$4 (\frac{- 41}{2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$2 (2) \frac{- 41}{2} + 3 (\frac{2}{6}) - \sqrt{4}$

Cancel the common factor.

$2 \cdot 2 \frac{- 41}{2} + 3 (\frac{2}{6}) - \sqrt{4}$

Rewrite the expression.

$2 \cdot - 41 + 3 (\frac{2}{6}) - \sqrt{4}$

Multiply $2$ by $- 41$ .

$- 82 + 3 (\frac{2}{6}) - \sqrt{4}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$- 82 + 3 \frac{2}{3 (2)} - \sqrt{4}$

Cancel the common factor.

$- 82 + 3 \frac{2}{3 \cdot 2} - \sqrt{4}$

Rewrite the expression.

$- 82 + \frac{2}{2} - \sqrt{4}$

Divide $2$ by $2$ .

$- 82 + 1 - \sqrt{4}$

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

$- 82 + 1 - \sqrt{2^{2}}$

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

$- 82 + 1 - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$- 82 + 1 - 2$

Step 2

Simplify by adding and subtracting.

Add $- 82$ and $1$ .

$- 81 - 2$

Subtract $2$ from $- 81$ .

$- 83$

Evaluate (4((3-5)^3-2(5/2)^2)+3(2/6))- square root of 4

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