Solve sqrt{1+(31/7)^2+(32/7)^2}

$$\sqrt { 1 + ( \frac { 31 } { 7 } ) ^ { 2 } + ( \frac { 32 } { 7 } ) ^ { 2 } }$$

Evaluate

$$\frac{3\sqrt{226}}{7}\approx 6.442841305$$

Solution Steps

Calculate \frac{31}{7} to the power of 2 and get \frac{961}{49}.

$$\sqrt{1+\frac{961}{49}+\left(\frac{32}{7}\right)^{2}}$$

Convert 1 to fraction \frac{49}{49}.

$$\sqrt{\frac{49}{49}+\frac{961}{49}+\left(\frac{32}{7}\right)^{2}}$$

Since \frac{49}{49} and \frac{961}{49} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{49+961}{49}+\left(\frac{32}{7}\right)^{2}}$$

Add 49 and 961 to get 1010.

$$\sqrt{\frac{1010}{49}+\left(\frac{32}{7}\right)^{2}}$$

Calculate \frac{32}{7} to the power of 2 and get \frac{1024}{49}.

$$\sqrt{\frac{1010}{49}+\frac{1024}{49}}$$

Since \frac{1010}{49} and \frac{1024}{49} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{1010+1024}{49}}$$

Add 1010 and 1024 to get 2034.

$$\sqrt{\frac{2034}{49}}$$

Rewrite the square root of the division \sqrt{\frac{2034}{49}} as the division of square roots \frac{\sqrt{2034}}{\sqrt{49}}.

$$\frac{\sqrt{2034}}{\sqrt{49}}$$

Factor 2034=3^{2}\times 226. Rewrite the square root of the product \sqrt{3^{2}\times 226} as the product of square roots \sqrt{3^{2}}\sqrt{226}. Take the square root of 3^{2}.

$$\frac{3\sqrt{226}}{\sqrt{49}}$$

Calculate the square root of 49 and get 7.

$$\frac{3\sqrt{226}}{7}$$