Solve 6(2-6div9)sqrt{6/9*6}

$$6(2-6 \div 9) \sqrt{ \frac{ 6 }{ 9 \times 6 } }$$

Evaluate

$$\frac{8}{3}\approx 2.666666667$$

Solution Steps

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$6\left(2-\frac{2}{3}\right)\sqrt{\frac{6}{9\times 6}}$$

Convert 2 to fraction \frac{6}{3}.

$$6\left(\frac{6}{3}-\frac{2}{3}\right)\sqrt{\frac{6}{9\times 6}}$$

Since \frac{6}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$6\times \frac{6-2}{3}\sqrt{\frac{6}{9\times 6}}$$

Subtract 2 from 6 to get 4.

$$6\times \frac{4}{3}\sqrt{\frac{6}{9\times 6}}$$

Express 6\times \frac{4}{3} as a single fraction.

$$\frac{6\times 4}{3}\sqrt{\frac{6}{9\times 6}}$$

Multiply 6 and 4 to get 24.

$$\frac{24}{3}\sqrt{\frac{6}{9\times 6}}$$

Divide 24 by 3 to get 8.

$$8\sqrt{\frac{6}{9\times 6}}$$

Multiply 9 and 6 to get 54.

$$8\sqrt{\frac{6}{54}}$$

Reduce the fraction \frac{6}{54} to lowest terms by extracting and canceling out 6.

$$8\sqrt{\frac{1}{9}}$$

Rewrite the square root of the division \frac{1}{9} as the division of square roots \frac{\sqrt{1}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$8\times \frac{1}{3}$$

Multiply 8 and \frac{1}{3} to get \frac{8}{3}.

$$\frac{8}{3}$$

Factor

$$\frac{2 ^ {3}}{3} = 2\frac{2}{3} = 2.6666666666666665$$