Solve 3/4sqrt{24}div9sqrt{2}*(2/3sqrt{32})

$$\frac { 3 } { 4 } \sqrt { 24 } \div 9 \sqrt { 2 } \times ( \frac { 2 } { 3 } \sqrt { 32 } )$$

Evaluate

$$\frac{8\sqrt{6}}{9}\approx 2.177324216$$

Solution Steps

Factor 32=2\times 16. Rewrite the square root of the product \sqrt{2\times 16} as the product of square roots \sqrt{2}\sqrt{16}.

$$\frac{\frac{3}{4}\sqrt{24}}{9}\sqrt{2}\times \frac{2}{3}\sqrt{2}\sqrt{16}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{\frac{3}{4}\sqrt{24}}{9}\times 2\times \frac{2}{3}\sqrt{16}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{\frac{3}{4}\times 2\sqrt{6}}{9}\times 2\times \frac{2}{3}\sqrt{16}$$

Express \frac{3}{4}\times 2 as a single fraction.

$$\frac{\frac{3\times 2}{4}\sqrt{6}}{9}\times 2\times \frac{2}{3}\sqrt{16}$$

Multiply 3 and 2 to get 6.

$$\frac{\frac{6}{4}\sqrt{6}}{9}\times 2\times \frac{2}{3}\sqrt{16}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{3}{2}\sqrt{6}}{9}\times 2\times \frac{2}{3}\sqrt{16}$$

Divide \frac{3}{2}\sqrt{6} by 9 to get \frac{1}{6}\sqrt{6}.

$$\frac{1}{6}\sqrt{6}\times 2\times \frac{2}{3}\sqrt{16}$$

Multiply \frac{1}{6} and 2 to get \frac{2}{6}.

$$\frac{2}{6}\sqrt{6}\times \frac{2}{3}\sqrt{16}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}\sqrt{6}\times \frac{2}{3}\sqrt{16}$$

Multiply \frac{1}{3} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 2}{3\times 3}\sqrt{6}\sqrt{16}$$

Do the multiplications in the fraction \frac{1\times 2}{3\times 3}.

$$\frac{2}{9}\sqrt{6}\sqrt{16}$$

Calculate the square root of 16 and get 4.

$$\frac{2}{9}\sqrt{6}\times 4$$

Express \frac{2}{9}\times 4 as a single fraction.

$$\frac{2\times 4}{9}\sqrt{6}$$

Multiply 2 and 4 to get 8.

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