Solve sqrt{(8/25)^2+28}

$$\sqrt { ( \frac { 8 } { 25 } ) ^ { 2 } + 28 }$$

Evaluate

$$\frac{2\sqrt{4391}}{25}\approx 5.301169682$$

Solution Steps

Calculate \frac{8}{25} to the power of 2 and get \frac{64}{625}.

$$\sqrt{\frac{64}{625}+28}$$

Convert 28 to fraction \frac{17500}{625}.

$$\sqrt{\frac{64}{625}+\frac{17500}{625}}$$

Since \frac{64}{625} and \frac{17500}{625} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{64+17500}{625}}$$

Add 64 and 17500 to get 17564.

$$\sqrt{\frac{17564}{625}}$$

Rewrite the square root of the division \sqrt{\frac{17564}{625}} as the division of square roots \frac{\sqrt{17564}}{\sqrt{625}}.

$$\frac{\sqrt{17564}}{\sqrt{625}}$$

Factor 17564=2^{2}\times 4391. Rewrite the square root of the product \sqrt{2^{2}\times 4391} as the product of square roots \sqrt{2^{2}}\sqrt{4391}. Take the square root of 2^{2}.

$$\frac{2\sqrt{4391}}{\sqrt{625}}$$

Calculate the square root of 625 and get 25.

$$\frac{2\sqrt{4391}}{25}$$