Solve frac{9sqrt{9}+3/2{9}^-frac{1{2}}}{9}

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

Evaluate

$$\frac{55}{18}\approx 3.055555556$$

Solution Steps

Calculate the square root of 9 and get 3.

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

Multiply 9 and 3 to get 27.

$$\frac{27+\frac{3}{2}\times 9^{-\frac{1}{2}}}{9}$$

Calculate 9 to the power of -\frac{1}{2} and get \frac{1}{3}.

$$\frac{27+\frac{3}{2}\times \frac{1}{3}}{9}$$

Multiply \frac{3}{2} and \frac{1}{3} to get \frac{1}{2}.

$$\frac{27+\frac{1}{2}}{9}$$

Add 27 and \frac{1}{2} to get \frac{55}{2}.

$$\frac{\frac{55}{2}}{9}$$

Express \frac{\frac{55}{2}}{9} as a single fraction.

$$\frac{55}{2\times 9}$$

Multiply 2 and 9 to get 18.

$$\frac{55}{18}$$

Factor

$$\frac{5 \cdot 11}{2 \cdot 3 ^ {2}} = 3\frac{1}{18} = 3.0555555555555554$$