Solve sqrt{111/25}+3sqrt{11/9}-0.6sqrt{3025}

$$\sqrt { 1 \frac { 11 } { 25 } } + 3 \sqrt { \frac { 11 } { 9 } } - 0.6 \sqrt { 3025 }$$

Evaluate

$$\sqrt{11}-31.8\approx -28.48337521$$

Solution Steps

Multiply 1 and 25 to get 25.

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

Add 25 and 11 to get 36.

$$\sqrt{\frac{36}{25}}+3\sqrt{\frac{11}{9}}-0.6\sqrt{3025}$$

Rewrite the square root of the division \frac{36}{25} as the division of square roots \frac{\sqrt{36}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{6}{5}+3\sqrt{\frac{11}{9}}-0.6\sqrt{3025}$$

Rewrite the square root of the division \sqrt{\frac{11}{9}} as the division of square roots \frac{\sqrt{11}}{\sqrt{9}}.

$$\frac{6}{5}+3\times \frac{\sqrt{11}}{\sqrt{9}}-0.6\sqrt{3025}$$

Calculate the square root of 9 and get 3.

$$\frac{6}{5}+3\times \frac{\sqrt{11}}{3}-0.6\sqrt{3025}$$

Cancel out 3 and 3.

$$\frac{6}{5}+\sqrt{11}-0.6\sqrt{3025}$$

Calculate the square root of 3025 and get 55.

$$\frac{6}{5}+\sqrt{11}-0.6\times 55$$

Multiply -0.6 and 55 to get -33.

$$\frac{6}{5}+\sqrt{11}-33$$

Convert 33 to fraction \frac{165}{5}.

$$\frac{6}{5}+\sqrt{11}-\frac{165}{5}$$

Since \frac{6}{5} and \frac{165}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-165}{5}+\sqrt{11}$$

Subtract 165 from 6 to get -159.

$$-\frac{159}{5}+\sqrt{11}$$