Solve sqrt{24}-sqrt{50/3}

$$\sqrt { 24 } - \sqrt { \frac { 50 } { 3 } }$$

Evaluate

$$\frac{\sqrt{6}}{3}\approx 0.816496581$$

Short Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$2\sqrt{6}-\sqrt{\frac{50}{3}}$$

Rewrite the square root of the division \sqrt{\frac{50}{3}} as the division of square roots \frac{\sqrt{50}}{\sqrt{3}}.

$$2\sqrt{6}-\frac{\sqrt{50}}{\sqrt{3}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$2\sqrt{6}-\frac{5\sqrt{2}}{\sqrt{3}}$$

Rationalize the denominator of \frac{5\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$2\sqrt{6}-\frac{5\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$2\sqrt{6}-\frac{5\sqrt{2}\sqrt{3}}{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$2\sqrt{6}-\frac{5\sqrt{6}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2\sqrt{6} times \frac{3}{3}.

$$\frac{3\times 2\sqrt{6}}{3}-\frac{5\sqrt{6}}{3}$$

Since \frac{3\times 2\sqrt{6}}{3} and \frac{5\sqrt{6}}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 2\sqrt{6}-5\sqrt{6}}{3}$$

Do the multiplications in 3\times 2\sqrt{6}-5\sqrt{6}.

$$\frac{6\sqrt{6}-5\sqrt{6}}{3}$$

Do the calculations in 6\sqrt{6}-5\sqrt{6}.

$$\frac{\sqrt{6}}{3}$$