Solve (7divsqrt{5})^2

$$( 7 \div \sqrt { 5 } ) ^ { 2 }$$

Evaluate

$$\frac{49}{5}=9.8$$

Solution Steps

Rationalize the denominator of \frac{7}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\left(\frac{7\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\right)^{2}$$

The square of \sqrt{5} is 5.

$$\left(\frac{7\sqrt{5}}{5}\right)^{2}$$

To raise \frac{7\sqrt{5}}{5} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(7\sqrt{5}\right)^{2}}{5^{2}}$$

Expand \left(7\sqrt{5}\right)^{2}.

$$\frac{7^{2}\left(\sqrt{5}\right)^{2}}{5^{2}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{49\left(\sqrt{5}\right)^{2}}{5^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{49\times 5}{5^{2}}$$

Multiply 49 and 5 to get 245.

$$\frac{245}{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{245}{25}$$

Reduce the fraction \frac{245}{25} to lowest terms by extracting and canceling out 5.

$$\frac{49}{5}$$

Factor

$$\frac{7 ^ {2}}{5} = 9\frac{4}{5} = 9.8$$