Solve sqrt{4^2+(4/7)^2}

$$\sqrt { 4 ^ { 2 } + ( \frac { 4 } { 7 } ) ^ { 2 } }$$

Evaluate

$$\frac{20\sqrt{2}}{7}\approx 4.040610178$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\sqrt{16+\left(\frac{4}{7}\right)^{2}}$$

Calculate \frac{4}{7} to the power of 2 and get \frac{16}{49}.

$$\sqrt{16+\frac{16}{49}}$$

Convert 16 to fraction \frac{784}{49}.

$$\sqrt{\frac{784}{49}+\frac{16}{49}}$$

Since \frac{784}{49} and \frac{16}{49} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{784+16}{49}}$$

Add 784 and 16 to get 800.

$$\sqrt{\frac{800}{49}}$$

Rewrite the square root of the division \sqrt{\frac{800}{49}} as the division of square roots \frac{\sqrt{800}}{\sqrt{49}}.

$$\frac{\sqrt{800}}{\sqrt{49}}$$

Factor 800=20^{2}\times 2. Rewrite the square root of the product \sqrt{20^{2}\times 2} as the product of square roots \sqrt{20^{2}}\sqrt{2}. Take the square root of 20^{2}.

$$\frac{20\sqrt{2}}{\sqrt{49}}$$

Calculate the square root of 49 and get 7.

$$\frac{20\sqrt{2}}{7}$$