Solve sqrt{111/25}+3sqrt{71/9}-0.6sqrt{3025}

$$\sqrt{ 1 \frac{ 11 }{ 25 } } +3 \sqrt{ 7 \frac{ 1 }{ 9 } } -0.6 \sqrt{ 3025 }$$

Evaluate

$$-23.8$$

Solution Steps

Multiply 1 and 25 to get 25.

$$\sqrt{\frac{25+11}{25}}+3\sqrt{\frac{7\times 9+1}{9}}-0.6\sqrt{3025}$$

Add 25 and 11 to get 36.

$$\sqrt{\frac{36}{25}}+3\sqrt{\frac{7\times 9+1}{9}}-0.6\sqrt{3025}$$

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.

$$\frac{6}{5}+3\sqrt{\frac{7\times 9+1}{9}}-0.6\sqrt{3025}$$

Multiply 7 and 9 to get 63.

$$\frac{6}{5}+3\sqrt{\frac{63+1}{9}}-0.6\sqrt{3025}$$

Add 63 and 1 to get 64.

$$\frac{6}{5}+3\sqrt{\frac{64}{9}}-0.6\sqrt{3025}$$

Rewrite the square root of the division \frac{64}{9} as the division of square roots \frac{\sqrt{64}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{6}{5}+3\times \frac{8}{3}-0.6\sqrt{3025}$$

Cancel out 3 and 3.

$$\frac{6}{5}+8-0.6\sqrt{3025}$$

Convert 8 to fraction \frac{40}{5}.

$$\frac{6}{5}+\frac{40}{5}-0.6\sqrt{3025}$$

Since \frac{6}{5} and \frac{40}{5} have the same denominator, add them by adding their numerators.

$$\frac{6+40}{5}-0.6\sqrt{3025}$$

Add 6 and 40 to get 46.

$$\frac{46}{5}-0.6\sqrt{3025}$$

Calculate the square root of 3025 and get 55.

$$\frac{46}{5}-0.6\times 55$$

Multiply -0.6 and 55 to get -33.

$$\frac{46}{5}-33$$

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

$$\frac{46}{5}-\frac{165}{5}$$

Since \frac{46}{5} and \frac{165}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{46-165}{5}$$

Subtract 165 from 46 to get -119.

$$-\frac{119}{5}$$

Factor

$$-23.8$$