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

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

Evaluate

$$4$$

Solution Steps

Calculate \frac{12}{5} to the power of 2 and get \frac{144}{25}.

$$\sqrt{\frac{144}{25}+\left(\frac{16}{5}\right)^{2}}$$

Calculate \frac{16}{5} to the power of 2 and get \frac{256}{25}.

$$\sqrt{\frac{144}{25}+\frac{256}{25}}$$

Since \frac{144}{25} and \frac{256}{25} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{144+256}{25}}$$

Add 144 and 256 to get 400.

$$\sqrt{\frac{400}{25}}$$

Divide 400 by 25 to get 16.

$$\sqrt{16}$$

Calculate the square root of 16 and get 4.

$$4$$

Factor

$$2^{2}$$