Solve sqrt{(2-16/5)^2+(6-12/5)^2}

$$\sqrt { ( 2 - \frac { 16 } { 5 } ) ^ { 2 } + ( 6 - \frac { 12 } { 5 } ) ^ { 2 } }$$

Evaluate

$$\frac{6\sqrt{10}}{5}\approx 3.794733192$$

Solution Steps

Subtract \frac{16}{5} from 2 to get -\frac{6}{5}.

$$\sqrt{\left(-\frac{6}{5}\right)^{2}+\left(6-\frac{12}{5}\right)^{2}}$$

Calculate -\frac{6}{5} to the power of 2 and get \frac{36}{25}.

$$\sqrt{\frac{36}{25}+\left(6-\frac{12}{5}\right)^{2}}$$

Subtract \frac{12}{5} from 6 to get \frac{18}{5}.

$$\sqrt{\frac{36}{25}+\left(\frac{18}{5}\right)^{2}}$$

Calculate \frac{18}{5} to the power of 2 and get \frac{324}{25}.

$$\sqrt{\frac{36}{25}+\frac{324}{25}}$$

Add \frac{36}{25} and \frac{324}{25} to get \frac{72}{5}.

$$\sqrt{\frac{72}{5}}$$

Rewrite the square root of the division \sqrt{\frac{72}{5}} as the division of square roots \frac{\sqrt{72}}{\sqrt{5}}.

$$\frac{\sqrt{72}}{\sqrt{5}}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$\frac{6\sqrt{2}}{\sqrt{5}}$$

Rationalize the denominator of \frac{6\sqrt{2}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{6\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{6\sqrt{2}\sqrt{5}}{5}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{6\sqrt{10}}{5}$$