Solve sqrt{(3/7+5)^2+(24/7)^2}

$$\sqrt { ( \frac { 3 } { 7 } + 5 ) ^ { 2 } + ( \frac { 24 } { 7 } ) ^ { 2 } }$$

Evaluate

$$\frac{2\sqrt{505}}{7}\approx 6.420630015$$

Solution Steps

Add \frac{3}{7} and 5 to get \frac{38}{7}.

$$\sqrt{\left(\frac{38}{7}\right)^{2}+\left(\frac{24}{7}\right)^{2}}$$

Calculate \frac{38}{7} to the power of 2 and get \frac{1444}{49}.

$$\sqrt{\frac{1444}{49}+\left(\frac{24}{7}\right)^{2}}$$

Calculate \frac{24}{7} to the power of 2 and get \frac{576}{49}.

$$\sqrt{\frac{1444}{49}+\frac{576}{49}}$$

Add \frac{1444}{49} and \frac{576}{49} to get \frac{2020}{49}.

$$\sqrt{\frac{2020}{49}}$$

Rewrite the square root of the division \sqrt{\frac{2020}{49}} as the division of square roots \frac{\sqrt{2020}}{\sqrt{49}}.

$$\frac{\sqrt{2020}}{\sqrt{49}}$$

Factor 2020=2^{2}\times 505. Rewrite the square root of the product \sqrt{2^{2}\times 505} as the product of square roots \sqrt{2^{2}}\sqrt{505}. Take the square root of 2^{2}.

$$\frac{2\sqrt{505}}{\sqrt{49}}$$

Calculate the square root of 49 and get 7.

$$\frac{2\sqrt{505}}{7}$$