Solve sqrt{2/3}*6/4-10/4

$$\sqrt { \frac { 2 } { 3 } } \times \frac { 6 } { 4 } - \frac { 10 } { 4 }$$

Evaluate

$$\frac{\sqrt{6}-5}{2}\approx -1.275255129$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{2}{3}} as the division of square roots \frac{\sqrt{2}}{\sqrt{3}}.

$$\frac{\sqrt{2}}{\sqrt{3}}\times \frac{6}{4}-\frac{10}{4}$$

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

$$\frac{\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\times \frac{6}{4}-\frac{10}{4}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{2}\sqrt{3}}{3}\times \frac{6}{4}-\frac{10}{4}$$

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

$$\frac{\sqrt{6}}{3}\times \frac{6}{4}-\frac{10}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\sqrt{6}}{3}\times \frac{3}{2}-\frac{10}{4}$$

Multiply \frac{\sqrt{6}}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{6}\times 3}{3\times 2}-\frac{10}{4}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\sqrt{6}}{2}-\frac{10}{4}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

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

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

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

Factor

$$\frac{\sqrt{6} - 5}{2} = -1.275255128608411$$