Solve sqrt{1+(4/5)^2}

$$\sqrt { 1 + ( \frac { 4 } { 5 } ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{41}}{5}\approx 1.280624847$$

Solution Steps

Calculate \frac{4}{5} to the power of 2 and get \frac{16}{25}.

$$\sqrt{1+\frac{16}{25}}$$

Convert 1 to fraction \frac{25}{25}.

$$\sqrt{\frac{25}{25}+\frac{16}{25}}$$

Since \frac{25}{25} and \frac{16}{25} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{25+16}{25}}$$

Add 25 and 16 to get 41.

$$\sqrt{\frac{41}{25}}$$

Rewrite the square root of the division \sqrt{\frac{41}{25}} as the division of square roots \frac{\sqrt{41}}{\sqrt{25}}.

$$\frac{\sqrt{41}}{\sqrt{25}}$$

Calculate the square root of 25 and get 5.

$$\frac{\sqrt{41}}{5}$$