Solve sqrt{-66/25+22}-5/3*(-66/25)=

$$\sqrt { - \frac { 66 } { 25 } + 22 } - \frac { 5 } { 3 } \cdot ( - \frac { 66 } { 25 } ) =$$

Evaluate

$$\frac{44}{5}=8.8$$

Solution Steps

Convert 22 to fraction \frac{550}{25}.

$$\sqrt{-\frac{66}{25}+\frac{550}{25}}-\frac{5}{3}\left(-\frac{66}{25}\right)$$

Since -\frac{66}{25} and \frac{550}{25} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{-66+550}{25}}-\frac{5}{3}\left(-\frac{66}{25}\right)$$

Add -66 and 550 to get 484.

$$\sqrt{\frac{484}{25}}-\frac{5}{3}\left(-\frac{66}{25}\right)$$

Rewrite the square root of the division \frac{484}{25} as the division of square roots \frac{\sqrt{484}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{22}{5}-\frac{5}{3}\left(-\frac{66}{25}\right)$$

Multiply \frac{5}{3} times -\frac{66}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22}{5}-\frac{5\left(-66\right)}{3\times 25}$$

Do the multiplications in the fraction \frac{5\left(-66\right)}{3\times 25}.

$$\frac{22}{5}-\frac{-330}{75}$$

Reduce the fraction \frac{-330}{75} to lowest terms by extracting and canceling out 15.

$$\frac{22}{5}-\left(-\frac{22}{5}\right)$$

The opposite of -\frac{22}{5} is \frac{22}{5}.

$$\frac{22}{5}+\frac{22}{5}$$

Since \frac{22}{5} and \frac{22}{5} have the same denominator, add them by adding their numerators.

$$\frac{22+22}{5}$$

Add 22 and 22 to get 44.

$$\frac{44}{5}$$

Factor

$$\frac{2 ^ {2} \cdot 11}{5} = 8\frac{4}{5} = 8.8$$