Solve 1/5+2/391/9-sqrt{1/3}*sqrt{frac{1}{3}}

$$\frac{ 1 }{ 5 } + \frac{ 2 }{ 3 } 9 \frac{ 1 }{ 9 } - \sqrt{ \frac{ 1 }{ 3 } } \times \sqrt{ \frac{ 1 }{ 3 } }$$

Evaluate

$$\frac{802}{135}\approx 5.940740741$$

Solution Steps

Multiply \sqrt{\frac{1}{3}} and \sqrt{\frac{1}{3}} to get \frac{1}{3}.

$$\frac{1}{5}+\frac{2}{3}\times \frac{9\times 9+1}{9}-\frac{1}{3}$$

Multiply 9 and 9 to get 81.

$$\frac{1}{5}+\frac{2}{3}\times \frac{81+1}{9}-\frac{1}{3}$$

Add 81 and 1 to get 82.

$$\frac{1}{5}+\frac{2}{3}\times \frac{82}{9}-\frac{1}{3}$$

Multiply \frac{2}{3} times \frac{82}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{5}+\frac{2\times 82}{3\times 9}-\frac{1}{3}$$

Do the multiplications in the fraction \frac{2\times 82}{3\times 9}.

$$\frac{1}{5}+\frac{164}{27}-\frac{1}{3}$$

Least common multiple of 5 and 27 is 135. Convert \frac{1}{5} and \frac{164}{27} to fractions with denominator 135.

$$\frac{27}{135}+\frac{820}{135}-\frac{1}{3}$$

Since \frac{27}{135} and \frac{820}{135} have the same denominator, add them by adding their numerators.

$$\frac{27+820}{135}-\frac{1}{3}$$

Add 27 and 820 to get 847.

$$\frac{847}{135}-\frac{1}{3}$$

Least common multiple of 135 and 3 is 135. Convert \frac{847}{135} and \frac{1}{3} to fractions with denominator 135.

$$\frac{847}{135}-\frac{45}{135}$$

Since \frac{847}{135} and \frac{45}{135} have the same denominator, subtract them by subtracting their numerators.

$$\frac{847-45}{135}$$

Subtract 45 from 847 to get 802.

$$\frac{802}{135}$$

Factor

$$\frac{2 \cdot 401}{3 ^ {3} \cdot 5} = 5\frac{127}{135} = 5.940740740740741$$