Solve sqrt{(48/10)^2+(7/10)^2}

$$\sqrt { ( \frac { 48 } { 10 } ) ^ { 2 } + ( \frac { 7 } { 10 } ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{2353}}{10}\approx 4.850773134$$

Solution Steps

Reduce the fraction \frac{48}{10} to lowest terms by extracting and canceling out 2.

$$\sqrt{\left(\frac{24}{5}\right)^{2}+\left(\frac{7}{10}\right)^{2}}$$

Calculate \frac{24}{5} to the power of 2 and get \frac{576}{25}.

$$\sqrt{\frac{576}{25}+\left(\frac{7}{10}\right)^{2}}$$

Calculate \frac{7}{10} to the power of 2 and get \frac{49}{100}.

$$\sqrt{\frac{576}{25}+\frac{49}{100}}$$

Add \frac{576}{25} and \frac{49}{100} to get \frac{2353}{100}.

$$\sqrt{\frac{2353}{100}}$$

Rewrite the square root of the division \sqrt{\frac{2353}{100}} as the division of square roots \frac{\sqrt{2353}}{\sqrt{100}}.

$$\frac{\sqrt{2353}}{\sqrt{100}}$$

Calculate the square root of 100 and get 10.

$$\frac{\sqrt{2353}}{10}$$