Solve 6sqrt{10/1000}-sqrt{124/25}

$$6 \sqrt { \frac { 10 } { 1000 } } - \sqrt { 1 \frac { 24 } { 25 } }$$

Evaluate

$$-\frac{4}{5}=-0.8$$

Solution Steps

Reduce the fraction \frac{10}{1000} to lowest terms by extracting and canceling out 10.

$$6\sqrt{\frac{1}{100}}-\sqrt{\frac{1\times 25+24}{25}}$$

Rewrite the square root of the division \frac{1}{100} as the division of square roots \frac{\sqrt{1}}{\sqrt{100}}. Take the square root of both numerator and denominator.

$$6\times \frac{1}{10}-\sqrt{\frac{1\times 25+24}{25}}$$

Multiply 6 and \frac{1}{10} to get \frac{6}{10}.

$$\frac{6}{10}-\sqrt{\frac{1\times 25+24}{25}}$$

Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{3}{5}-\sqrt{\frac{1\times 25+24}{25}}$$

Multiply 1 and 25 to get 25.

$$\frac{3}{5}-\sqrt{\frac{25+24}{25}}$$

Add 25 and 24 to get 49.

$$\frac{3}{5}-\sqrt{\frac{49}{25}}$$

Rewrite the square root of the division \frac{49}{25} as the division of square roots \frac{\sqrt{49}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{3}{5}-\frac{7}{5}$$

Since \frac{3}{5} and \frac{7}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-7}{5}$$

Subtract 7 from 3 to get -4.

$$-\frac{4}{5}$$

Factor

$$-\frac{4}{5} = -0.8$$