Evaluate (4((6-4)^2-3(1/3-4/5))+2)- square root of 49

$(4 ({(6 - 4)}^{2} - 3 (\frac{1}{3} - \frac{4}{5})) + 2) - \sqrt{49}$

Step 1

Simplify each term.

Subtract $4$ from $6$ .

$4 (2^{2} - 3 (\frac{1}{3} - \frac{4}{5})) + 2 - \sqrt{49}$

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

$4 (4 - 3 (\frac{1}{3} - \frac{4}{5})) + 2 - \sqrt{49}$

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$4 (4 - 3 (\frac{1}{3} \cdot \frac{5}{5} - \frac{4}{5})) + 2 - \sqrt{49}$

To write $- \frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$4 (4 - 3 (\frac{1}{3} \cdot \frac{5}{5} - \frac{4}{5} \cdot \frac{3}{3})) + 2 - \sqrt{49}$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$4 (4 - 3 (\frac{5}{3 \cdot 5} - \frac{4}{5} \cdot \frac{3}{3})) + 2 - \sqrt{49}$

Multiply $3$ by $5$ .

$4 (4 - 3 (\frac{5}{15} - \frac{4}{5} \cdot \frac{3}{3})) + 2 - \sqrt{49}$

Multiply $\frac{4}{5}$ by $\frac{3}{3}$ .

$4 (4 - 3 (\frac{5}{15} - \frac{4 \cdot 3}{5 \cdot 3})) + 2 - \sqrt{49}$

Multiply $5$ by $3$ .

$4 (4 - 3 (\frac{5}{15} - \frac{4 \cdot 3}{15})) + 2 - \sqrt{49}$

Combine the numerators over the common denominator.

$4 (4 - 3 \frac{5 - 4 \cdot 3}{15}) + 2 - \sqrt{49}$

Simplify the numerator.

Multiply $- 4$ by $3$ .

$4 (4 - 3 \frac{5 - 12}{15}) + 2 - \sqrt{49}$

Subtract $12$ from $5$ .

$4 (4 - 3 (\frac{- 7}{15})) + 2 - \sqrt{49}$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

$4 (4 + 3 (- 1) \frac{- 7}{15}) + 2 - \sqrt{49}$

Factor $3$ out of $15$ .

$4 (4 + 3 \cdot - 1 \frac{- 7}{3 \cdot 5}) + 2 - \sqrt{49}$

Cancel the common factor.

$4 (4 + 3 \cdot - 1 \frac{- 7}{3 \cdot 5}) + 2 - \sqrt{49}$

Rewrite the expression.

$4 (4 - 1 (\frac{- 7}{5})) + 2 - \sqrt{49}$

Move the negative in front of the fraction.

$4 (4 - 1 (- \frac{7}{5})) + 2 - \sqrt{49}$

Multiply $- 1 (- \frac{7}{5})$ .

Multiply $- 1$ by $- 1$ .

$4 (4 + 1 (\frac{7}{5})) + 2 - \sqrt{49}$

Multiply $\frac{7}{5}$ by $1$ .

$4 (4 + \frac{7}{5}) + 2 - \sqrt{49}$

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$4 (4 \cdot \frac{5}{5} + \frac{7}{5}) + 2 - \sqrt{49}$

Combine $4$ and $\frac{5}{5}$ .

$4 (\frac{4 \cdot 5}{5} + \frac{7}{5}) + 2 - \sqrt{49}$

Combine the numerators over the common denominator.

$4 \frac{4 \cdot 5 + 7}{5} + 2 - \sqrt{49}$

Simplify the numerator.

Multiply $4$ by $5$ .

$4 \frac{20 + 7}{5} + 2 - \sqrt{49}$

Add $20$ and $7$ .

$4 (\frac{27}{5}) + 2 - \sqrt{49}$

Multiply $4 (\frac{27}{5})$ .

Combine $4$ and $\frac{27}{5}$ .

$\frac{4 \cdot 27}{5} + 2 - \sqrt{49}$

Multiply $4$ by $27$ .

$\frac{108}{5} + 2 - \sqrt{49}$

Rewrite $49$ as $7^{2}$ .

$\frac{108}{5} + 2 - \sqrt{7^{2}}$

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

$\frac{108}{5} + 2 - 1 \cdot 7$

Multiply $- 1$ by $7$ .

$\frac{108}{5} + 2 - 7$

Step 2

Find the common denominator.

Write $2$ as a fraction with denominator $1$ .

$\frac{108}{5} + \frac{2}{1} - 7$

Multiply $\frac{2}{1}$ by $\frac{5}{5}$ .

$\frac{108}{5} + \frac{2}{1} \cdot \frac{5}{5} - 7$

Multiply $\frac{2}{1}$ by $\frac{5}{5}$ .

$\frac{108}{5} + \frac{2 \cdot 5}{5} - 7$

Write $- 7$ as a fraction with denominator $1$ .

$\frac{108}{5} + \frac{2 \cdot 5}{5} + \frac{- 7}{1}$

Multiply $\frac{- 7}{1}$ by $\frac{5}{5}$ .

$\frac{108}{5} + \frac{2 \cdot 5}{5} + \frac{- 7}{1} \cdot \frac{5}{5}$

Multiply $\frac{- 7}{1}$ by $\frac{5}{5}$ .

$\frac{108}{5} + \frac{2 \cdot 5}{5} + \frac{- 7 \cdot 5}{5}$

Step 3

Combine the numerators over the common denominator.

$\frac{108 + 2 \cdot 5 - 7 \cdot 5}{5}$

Step 4

Simplify each term.

Multiply $2$ by $5$ .

$\frac{108 + 10 - 7 \cdot 5}{5}$

Multiply $- 7$ by $5$ .

$\frac{108 + 10 - 35}{5}$

Step 5

Simplify by adding and subtracting.

Add $108$ and $10$ .

$\frac{118 - 35}{5}$

Subtract $35$ from $118$ .

$\frac{83}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{83}{5}$

Decimal Form:

$16.6$

Mixed Number Form:

$16 \frac{3}{5}$

Evaluate (4((6-4)^2-3(1/3-4/5))+2)- square root of 49

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