Solve sqrt{(25/7)^2+(50/7)^2}

$$\sqrt { ( \frac { 25 } { 7 } ) ^ { 2 } + ( \frac { 50 } { 7 } ) ^ { 2 } }$$

Evaluate

$$\frac{25\sqrt{5}}{7}\approx 7.985957062$$

Solution Steps

Calculate \frac{25}{7} to the power of 2 and get \frac{625}{49}.

$$\sqrt{\frac{625}{49}+\left(\frac{50}{7}\right)^{2}}$$

Calculate \frac{50}{7} to the power of 2 and get \frac{2500}{49}.

$$\sqrt{\frac{625}{49}+\frac{2500}{49}}$$

Since \frac{625}{49} and \frac{2500}{49} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{625+2500}{49}}$$

Add 625 and 2500 to get 3125.

$$\sqrt{\frac{3125}{49}}$$

Rewrite the square root of the division \sqrt{\frac{3125}{49}} as the division of square roots \frac{\sqrt{3125}}{\sqrt{49}}.

$$\frac{\sqrt{3125}}{\sqrt{49}}$$

Factor 3125=25^{2}\times 5. Rewrite the square root of the product \sqrt{25^{2}\times 5} as the product of square roots \sqrt{25^{2}}\sqrt{5}. Take the square root of 25^{2}.

$$\frac{25\sqrt{5}}{\sqrt{49}}$$

Calculate the square root of 49 and get 7.

$$\frac{25\sqrt{5}}{7}$$