Solve sqrt{11/25}+3sqrt{71/9}-0.6sqrt{3025}

$$\sqrt { \frac { 11 } { 25 } } + 3 \sqrt { \frac { 71 } { 9 } } - 0.6 \sqrt { 3025 }$$

Evaluate

$$\frac{\sqrt{11}}{5}+\sqrt{71}-33\approx -23.910525269$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{11}{25}} as the division of square roots \frac{\sqrt{11}}{\sqrt{25}}.

$$\frac{\sqrt{11}}{\sqrt{25}}+3\sqrt{\frac{71}{9}}-0.6\sqrt{3025}$$

Calculate the square root of 25 and get 5.

$$\frac{\sqrt{11}}{5}+3\sqrt{\frac{71}{9}}-0.6\sqrt{3025}$$

Rewrite the square root of the division \sqrt{\frac{71}{9}} as the division of square roots \frac{\sqrt{71}}{\sqrt{9}}.

$$\frac{\sqrt{11}}{5}+3\times \frac{\sqrt{71}}{\sqrt{9}}-0.6\sqrt{3025}$$

Calculate the square root of 9 and get 3.

$$\frac{\sqrt{11}}{5}+3\times \frac{\sqrt{71}}{3}-0.6\sqrt{3025}$$

Cancel out 3 and 3.

$$\frac{\sqrt{11}}{5}+\sqrt{71}-0.6\sqrt{3025}$$

Calculate the square root of 3025 and get 55.

$$\frac{\sqrt{11}}{5}+\sqrt{71}-0.6\times 55$$

Multiply -0.6 and 55 to get -33.

$$\frac{\sqrt{11}}{5}+\sqrt{71}-33$$

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{71}-33 times \frac{5}{5}.

$$\frac{\sqrt{11}}{5}+\frac{5\left(\sqrt{71}-33\right)}{5}$$

Since \frac{\sqrt{11}}{5} and \frac{5\left(\sqrt{71}-33\right)}{5} have the same denominator, add them by adding their numerators.

$$\frac{\sqrt{11}+5\left(\sqrt{71}-33\right)}{5}$$

Do the multiplications in \sqrt{11}+5\left(\sqrt{71}-33\right).

$$\frac{\sqrt{11}+5\sqrt{71}-165}{5}$$