Solve 12/5frac{6sqrt{33}}{11}+3/5*5.4/11

$$\frac { 12 } { 5 } \frac { 6 \sqrt { 33 } } { 11 } + \frac { 3 } { 5 } \cdot \frac { 5.4 } { 11 }$$

Evaluate

$$\frac{72\sqrt{33}}{55}+\frac{81}{275}\approx 7.814700192$$

Short Solution Steps

Multiply \frac{12}{5} times \frac{6\sqrt{33}}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12\times 6\sqrt{33}}{5\times 11}+\frac{3}{5}\times \frac{5.4}{11}$$

Expand \frac{5.4}{11} by multiplying both numerator and the denominator by 10.

$$\frac{12\times 6\sqrt{33}}{5\times 11}+\frac{3}{5}\times \frac{54}{110}$$

Reduce the fraction \frac{54}{110} to lowest terms by extracting and canceling out 2.

$$\frac{12\times 6\sqrt{33}}{5\times 11}+\frac{3}{5}\times \frac{27}{55}$$

Multiply \frac{3}{5} times \frac{27}{55} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12\times 6\sqrt{33}}{5\times 11}+\frac{3\times 27}{5\times 55}$$

Do the multiplications in the fraction \frac{3\times 27}{5\times 55}.

$$\frac{12\times 6\sqrt{33}}{5\times 11}+\frac{81}{275}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5\times 11 and 275 is 275. Multiply \frac{12\times 6\sqrt{33}}{5\times 11} times \frac{5}{5}.

$$\frac{5\times 12\times 6\sqrt{33}}{275}+\frac{81}{275}$$

Since \frac{5\times 12\times 6\sqrt{33}}{275} and \frac{81}{275} have the same denominator, add them by adding their numerators.

$$\frac{5\times 12\times 6\sqrt{33}+81}{275}$$

Do the multiplications in 5\times 12\times 6\sqrt{33}+81.

$$\frac{360\sqrt{33}+81}{275}$$

Factor

$$\frac{9 {(40 \sqrt{33} + 9)}}{275} = 7.8147001918316015$$