Solve sqrt{2}divsqrt{48}*sqrt{6}

$$\sqrt{ 2 } \div \sqrt{ 48 } \times \sqrt{ 6 }$$

Evaluate

$$\frac{1}{2}=0.5$$

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}.

$$\frac{\sqrt{2}}{4\sqrt{3}}\sqrt{6}$$

Rationalize the denominator of \frac{\sqrt{2}}{4\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{2}\sqrt{3}}{4\left(\sqrt{3}\right)^{2}}\sqrt{6}$$

The square of \sqrt{3} is 3.

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

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

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

Multiply 4 and 3 to get 12.

$$\frac{\sqrt{6}}{12}\sqrt{6}$$

Express \frac{\sqrt{6}}{12}\sqrt{6} as a single fraction.

$$\frac{\sqrt{6}\sqrt{6}}{12}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{6}{12}$$

Reduce the fraction \frac{6}{12} to lowest terms by extracting and canceling out 6.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$