Solve sqrt{214/25}-sqrt{121/100}

$$\sqrt { 2 \frac { 14 } { 25 } } - \sqrt { 1 \frac { 21 } { 100 } }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Multiply 2 and 25 to get 50.

$$\sqrt{\frac{50+14}{25}}-\sqrt{\frac{1\times 100+21}{100}}$$

Add 50 and 14 to get 64.

$$\sqrt{\frac{64}{25}}-\sqrt{\frac{1\times 100+21}{100}}$$

Rewrite the square root of the division \frac{64}{25} as the division of square roots \frac{\sqrt{64}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{8}{5}-\sqrt{\frac{1\times 100+21}{100}}$$

Multiply 1 and 100 to get 100.

$$\frac{8}{5}-\sqrt{\frac{100+21}{100}}$$

Add 100 and 21 to get 121.

$$\frac{8}{5}-\sqrt{\frac{121}{100}}$$

Rewrite the square root of the division \frac{121}{100} as the division of square roots \frac{\sqrt{121}}{\sqrt{100}}. Take the square root of both numerator and denominator.

$$\frac{8}{5}-\frac{11}{10}$$

Least common multiple of 5 and 10 is 10. Convert \frac{8}{5} and \frac{11}{10} to fractions with denominator 10.

$$\frac{16}{10}-\frac{11}{10}$$

Since \frac{16}{10} and \frac{11}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-11}{10}$$

Subtract 11 from 16 to get 5.

$$\frac{5}{10}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$