Solve 7/2+sqrt{49.{left(-frac{4/5right)}^2{left(5/2right)}^2}}{5/2}

$$\frac{ \frac{ 7 }{ 2 } + \sqrt{ 49. { \left(- \frac{ 4 }{ 5 } \right) }^{ 2 } { \left( \frac{ 5 }{ 2 } \right) }^{ 2 } } }{ \frac{ 5 }{ 2 } }$$

Evaluate

$$7$$

Solution Steps

Calculate -\frac{4}{5} to the power of 2 and get \frac{16}{25}.

$$\frac{\frac{7}{2}+\sqrt{49\times \frac{16}{25}\times \left(\frac{5}{2}\right)^{2}}}{\frac{5}{2}}$$

Express 49\times \frac{16}{25} as a single fraction.

$$\frac{\frac{7}{2}+\sqrt{\frac{49\times 16}{25}\times \left(\frac{5}{2}\right)^{2}}}{\frac{5}{2}}$$

Multiply 49 and 16 to get 784.

$$\frac{\frac{7}{2}+\sqrt{\frac{784}{25}\times \left(\frac{5}{2}\right)^{2}}}{\frac{5}{2}}$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{\frac{7}{2}+\sqrt{\frac{784}{25}\times \frac{25}{4}}}{\frac{5}{2}}$$

Multiply \frac{784}{25} times \frac{25}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7}{2}+\sqrt{\frac{784\times 25}{25\times 4}}}{\frac{5}{2}}$$

Cancel out 25 in both numerator and denominator.

$$\frac{\frac{7}{2}+\sqrt{\frac{784}{4}}}{\frac{5}{2}}$$

Divide 784 by 4 to get 196.

$$\frac{\frac{7}{2}+\sqrt{196}}{\frac{5}{2}}$$

Calculate the square root of 196 and get 14.

$$\frac{\frac{7}{2}+14}{\frac{5}{2}}$$

Convert 14 to fraction \frac{28}{2}.

$$\frac{\frac{7}{2}+\frac{28}{2}}{\frac{5}{2}}$$

Since \frac{7}{2} and \frac{28}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7+28}{2}}{\frac{5}{2}}$$

Add 7 and 28 to get 35.

$$\frac{\frac{35}{2}}{\frac{5}{2}}$$

Divide \frac{35}{2} by \frac{5}{2} by multiplying \frac{35}{2} by the reciprocal of \frac{5}{2}.

$$\frac{35}{2}\times \frac{2}{5}$$

Multiply \frac{35}{2} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35\times 2}{2\times 5}$$

Cancel out 2 in both numerator and denominator.

$$\frac{35}{5}$$

Divide 35 by 5 to get 7.

$$7$$

Factor

$$7$$