Solve sqrt{3/14*28/9+10/9}

$$\sqrt { \frac { 3 } { 14 } \cdot \frac { 28 } { 9 } + \frac { 10 } { 9 } }$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

Multiply \frac{3}{14} times \frac{28}{9} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{3\times 28}{14\times 9}+\frac{10}{9}}$$

Do the multiplications in the fraction \frac{3\times 28}{14\times 9}.

$$\sqrt{\frac{84}{126}+\frac{10}{9}}$$

Reduce the fraction \frac{84}{126} to lowest terms by extracting and canceling out 42.

$$\sqrt{\frac{2}{3}+\frac{10}{9}}$$

Least common multiple of 3 and 9 is 9. Convert \frac{2}{3} and \frac{10}{9} to fractions with denominator 9.

$$\sqrt{\frac{6}{9}+\frac{10}{9}}$$

Since \frac{6}{9} and \frac{10}{9} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{6+10}{9}}$$

Add 6 and 10 to get 16.

$$\sqrt{\frac{16}{9}}$$

Rewrite the square root of the division \frac{16}{9} as the division of square roots \frac{\sqrt{16}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$