Solve sqrt{12/3}-sqrt{5/8}

$$\sqrt { 1 \frac { 2 } { 3 } } - \sqrt { \frac { 5 } { 8 } }$$

Evaluate

$$\frac{\sqrt{15}}{3}-\frac{\sqrt{10}}{4}\approx 0.500425034$$

Short Solution Steps

Multiply 1 and 3 to get 3.

$$\sqrt{\frac{3+2}{3}}-\sqrt{\frac{5}{8}}$$

Add 3 and 2 to get 5.

$$\sqrt{\frac{5}{3}}-\sqrt{\frac{5}{8}}$$

Rewrite the square root of the division \sqrt{\frac{5}{3}} as the division of square roots \frac{\sqrt{5}}{\sqrt{3}}.

$$\frac{\sqrt{5}}{\sqrt{3}}-\sqrt{\frac{5}{8}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-\sqrt{\frac{5}{8}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{5}\sqrt{3}}{3}-\sqrt{\frac{5}{8}}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{15}}{3}-\sqrt{\frac{5}{8}}$$

Rewrite the square root of the division \sqrt{\frac{5}{8}} as the division of square roots \frac{\sqrt{5}}{\sqrt{8}}.

$$\frac{\sqrt{15}}{3}-\frac{\sqrt{5}}{\sqrt{8}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{\sqrt{15}}{3}-\frac{\sqrt{5}}{2\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{5}}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{15}}{3}-\frac{\sqrt{5}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{15}}{3}-\frac{\sqrt{5}\sqrt{2}}{2\times 2}$$

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

$$\frac{\sqrt{15}}{3}-\frac{\sqrt{10}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{15}}{3}-\frac{\sqrt{10}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 4 is 12. Multiply \frac{\sqrt{15}}{3} times \frac{4}{4}. Multiply \frac{\sqrt{10}}{4} times \frac{3}{3}.

$$\frac{4\sqrt{15}}{12}-\frac{3\sqrt{10}}{12}$$

Since \frac{4\sqrt{15}}{12} and \frac{3\sqrt{10}}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\sqrt{15}-3\sqrt{10}}{12}$$