Solve frac{sqrt{2}+10/3}{6/5}

$$\frac { \sqrt { 2 } + \frac { 10 } { 3 } } { \frac { 6 } { 5 } }$$

Evaluate

$$\frac{5\sqrt{2}}{6}+\frac{25}{9}\approx 3.95628908$$

Solution Steps

Divide \sqrt{2}+\frac{10}{3} by \frac{6}{5} by multiplying \sqrt{2}+\frac{10}{3} by the reciprocal of \frac{6}{5}.

$$\frac{\left(\sqrt{2}+\frac{10}{3}\right)\times 5}{6}$$

Use the distributive property to multiply \sqrt{2}+\frac{10}{3} by 5.

$$\frac{5\sqrt{2}+\frac{10}{3}\times 5}{6}$$

Express \frac{10}{3}\times 5 as a single fraction.

$$\frac{5\sqrt{2}+\frac{10\times 5}{3}}{6}$$

Multiply 10 and 5 to get 50.

$$\frac{5\sqrt{2}+\frac{50}{3}}{6}$$

Factor

$$\frac{5 {(3 \sqrt{2} + 10)}}{18} = 3.956289079755357$$