Solve 8/15*3/2+sqrt{2/3}*sqrt{2/3}

$$\frac { 8 } { 15 } \cdot \frac { 3 } { 2 } + \sqrt { \frac { 2 } { 3 } } \cdot \sqrt { \frac { 2 } { 3 } }$$

Evaluate

$$\frac{22}{15}\approx 1.466666667$$

Solution Steps

Multiply \sqrt{\frac{2}{3}} and \sqrt{\frac{2}{3}} to get \frac{2}{3}.

$$\frac{8}{15}\times \frac{3}{2}+\frac{2}{3}$$

Multiply \frac{8}{15} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 3}{15\times 2}+\frac{2}{3}$$

Do the multiplications in the fraction \frac{8\times 3}{15\times 2}.

$$\frac{24}{30}+\frac{2}{3}$$

Reduce the fraction \frac{24}{30} to lowest terms by extracting and canceling out 6.

$$\frac{4}{5}+\frac{2}{3}$$

Least common multiple of 5 and 3 is 15. Convert \frac{4}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{12}{15}+\frac{10}{15}$$

Since \frac{12}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$\frac{12+10}{15}$$

Add 12 and 10 to get 22.

$$\frac{22}{15}$$

Factor

$$\frac{2 \cdot 11}{3 \cdot 5} = 1\frac{7}{15} = 1.4666666666666666$$