Solve 1/2sqrt{48}div(3sqrt{2}*sqrt{3})

$$\frac { 1 } { 2 } \sqrt { 48 } \div ( 3 \sqrt { 2 } \times \sqrt { 3 } )$$

Evaluate

$$\frac{\sqrt{2}}{3}\approx 0.471404521$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{\frac{1}{2}\times 4\sqrt{3}}{3\sqrt{2}\sqrt{3}}$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$\frac{\frac{4}{2}\sqrt{3}}{3\sqrt{2}\sqrt{3}}$$

Divide 4 by 2 to get 2.

$$\frac{2\sqrt{3}}{3\sqrt{2}\sqrt{3}}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

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

Rationalize the denominator of \frac{2\sqrt{3}}{3\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{2\sqrt{3}\sqrt{6}}{3\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

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

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

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

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

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

Multiply 3 and 6 to get 18.

$$\frac{2\times 3\sqrt{2}}{18}$$

Multiply 2 and 3 to get 6.

$$\frac{6\sqrt{2}}{18}$$

Divide 6\sqrt{2} by 18 to get \frac{1}{3}\sqrt{2}.

$$\frac{1}{3}\sqrt{2}$$