Solve sqrt{5/2}*sqrt{5/8}-sqrt{3/7}*sqrt{12/7}

$$\sqrt { \frac { 5 } { 2 } } \cdot \sqrt { \frac { 5 } { 8 } } - \sqrt { \frac { 3 } { 7 } } \cdot \sqrt { \frac { 12 } { 7 } }$$

Evaluate

$$\frac{11}{28}\approx 0.392857143$$

Solution Steps

To multiply \sqrt{\frac{5}{2}} and \sqrt{\frac{5}{8}}, multiply the numbers under the square root.

$$\sqrt{\frac{25}{16}}-\sqrt{\frac{3}{7}}\sqrt{\frac{12}{7}}$$

Rewrite the square root of the division \frac{25}{16} as the division of square roots \frac{\sqrt{25}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{5}{4}-\sqrt{\frac{3}{7}}\sqrt{\frac{12}{7}}$$

To multiply \sqrt{\frac{3}{7}} and \sqrt{\frac{12}{7}}, multiply the numbers under the square root.

$$\frac{5}{4}-\sqrt{\frac{36}{49}}$$

Rewrite the square root of the division \frac{36}{49} as the division of square roots \frac{\sqrt{36}}{\sqrt{49}}. Take the square root of both numerator and denominator.

$$\frac{5}{4}-\frac{6}{7}$$

Least common multiple of 4 and 7 is 28. Convert \frac{5}{4} and \frac{6}{7} to fractions with denominator 28.

$$\frac{35}{28}-\frac{24}{28}$$

Since \frac{35}{28} and \frac{24}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-24}{28}$$

Subtract 24 from 35 to get 11.

$$\frac{11}{28}$$

Factor

$$\frac{11}{2 ^ {2} \cdot 7} = 0.39285714285714285$$