Simplify 12.65÷(-2.3)+6^2- square root of 49

$12.65 \div (- 2.3) + 6^{2} - \sqrt{49}$

Step 1

Find the common denominator.

Multiply $12.65 \div (- 2.3)$ by $\frac{\frac{23}{- 2.3}}{\frac{23}{- 2.3}}$ .

$12.65 \div (- 2.3) \cdot \frac{\frac{23}{- 2.3}}{\frac{23}{- 2.3}} + 6^{2} - \sqrt{49}$

Multiply $12.65 \div (- 2.3)$ by $\frac{\frac{23}{- 2.3}}{\frac{23}{- 2.3}}$ .

$\frac{12.65 (\frac{23}{- 2.3})}{- 2.3 (\frac{23}{- 2.3})} + 6^{2} - \sqrt{49}$

Write $6^{2}$ as a fraction with denominator $1$ .

$\frac{12.65 (\frac{23}{- 2.3})}{- 2.3 (\frac{23}{- 2.3})} + \frac{6^{2}}{1} - \sqrt{49}$

Multiply $\frac{6^{2}}{1}$ by $\frac{23}{23}$ .

$\frac{12.65 (\frac{23}{- 2.3})}{- 2.3 (\frac{23}{- 2.3})} + \frac{6^{2}}{1} \cdot \frac{23}{23} - \sqrt{49}$

Multiply $\frac{6^{2}}{1}$ by $\frac{23}{23}$ .

$\frac{12.65 (\frac{23}{- 2.3})}{- 2.3 (\frac{23}{- 2.3})} + \frac{6^{2} \cdot 23}{23} - \sqrt{49}$

Write $- \sqrt{49}$ as a fraction with denominator $1$ .

$\frac{12.65 (\frac{23}{- 2.3})}{- 2.3 (\frac{23}{- 2.3})} + \frac{6^{2} \cdot 23}{23} + \frac{- \sqrt{49}}{1}$

Multiply $\frac{- \sqrt{49}}{1}$ by $\frac{23}{23}$ .

$\frac{12.65 (\frac{23}{- 2.3})}{- 2.3 (\frac{23}{- 2.3})} + \frac{6^{2} \cdot 23}{23} + \frac{- \sqrt{49}}{1} \cdot \frac{23}{23}$

Multiply $\frac{- \sqrt{49}}{1}$ by $\frac{23}{23}$ .

$\frac{12.65 (\frac{23}{- 2.3})}{- 2.3 (\frac{23}{- 2.3})} + \frac{6^{2} \cdot 23}{23} + \frac{- \sqrt{49} \cdot 23}{23}$

Combine $- 2.3$ and $\frac{23}{- 2.3}$ .

$\frac{12.65 (\frac{23}{- 2.3})}{\frac{- 2.3 \cdot 23}{- 2.3}} + \frac{6^{2} \cdot 23}{23} + \frac{- \sqrt{49} \cdot 23}{23}$

Multiply $- 2.3$ by $23$ .

$\frac{12.65 (\frac{23}{- 2.3})}{\frac{- 52.9}{- 2.3}} + \frac{6^{2} \cdot 23}{23} + \frac{- \sqrt{49} \cdot 23}{23}$

Step 2

Combine the numerators over the common denominator.

$\frac{12.65 (\frac{23}{- 2.3})}{\frac{- 52.9}{- 2.3}} + \frac{6^{2} \cdot 23 - \sqrt{49} \cdot 23}{23}$

Step 3

Simplify each term.

Raise $6$ to the power of $2$ .

$\frac{12.65 (\frac{23}{- 2.3})}{\frac{- 52.9}{- 2.3}} + \frac{36 \cdot 23 - \sqrt{49} \cdot 23}{23}$

Multiply $36$ by $23$ .

$\frac{12.65 (\frac{23}{- 2.3})}{\frac{- 52.9}{- 2.3}} + \frac{828 - \sqrt{49} \cdot 23}{23}$

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

$\frac{12.65 (\frac{23}{- 2.3})}{\frac{- 52.9}{- 2.3}} + \frac{828 - \sqrt{7^{2}} \cdot 23}{23}$

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

$\frac{12.65 (\frac{23}{- 2.3})}{\frac{- 52.9}{- 2.3}} + \frac{828 - 1 \cdot 7 \cdot 23}{23}$

Multiply $- 1 \cdot 7 \cdot 23$ .

Multiply $- 1$ by $7$ .

$\frac{12.65 (\frac{23}{- 2.3})}{\frac{- 52.9}{- 2.3}} + \frac{828 - 7 \cdot 23}{23}$

Multiply $- 7$ by $23$ .

$\frac{12.65 (\frac{23}{- 2.3})}{\frac{- 52.9}{- 2.3}} + \frac{828 - 161}{23}$

Step 4

Subtract $161$ from $828$ .

$\frac{12.65 (\frac{23}{- 2.3})}{\frac{- 52.9}{- 2.3}} + \frac{667}{23}$

Step 5

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$12.65 (\frac{23}{- 2.3}) \frac{- 2.3}{- 52.9} + \frac{667}{23}$

Divide $23$ by $- 2.3$ .

$12.65 \cdot - 10 \frac{- 2.3}{- 52.9} + \frac{667}{23}$

Multiply $12.65$ by $- 10$ .

$- 126.5 (\frac{- 2.3}{- 52.9}) + \frac{667}{23}$

Divide $- 2.3$ by $- 52.9$ .

$- 126.5 \cdot 0.04347826 + \frac{667}{23}$

Multiply $- 126.5$ by $0.04347826$ .

$- 5.5 + \frac{667}{23}$

Divide $667$ by $23$ .

$- 5.5 + 29$

Step 6

Add $- 5.5$ and $29$ .

$23.5$

Simplify 12.65÷(-2.3)+6^2- square root of 49

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