Solve sqrt{53/25}

$$\sqrt { 5 \frac { 3 } { 25 } }$$

Evaluate

$$\frac{8\sqrt{2}}{5}\approx 2.2627417$$

Solution Steps

Multiply 5 and 25 to get 125.

$$\sqrt{\frac{125+3}{25}}$$

Add 125 and 3 to get 128.

$$\sqrt{\frac{128}{25}}$$

Rewrite the square root of the division \sqrt{\frac{128}{25}} as the division of square roots \frac{\sqrt{128}}{\sqrt{25}}.

$$\frac{\sqrt{128}}{\sqrt{25}}$$

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

$$\frac{8\sqrt{2}}{\sqrt{25}}$$

Calculate the square root of 25 and get 5.

$$\frac{8\sqrt{2}}{5}$$