Solve 3sqrt{2}*1/2sqrt{6}divsqrt{18}

$$3 \sqrt{ 2 } \times \frac{ 1 }{ 2 } \sqrt{ 6 } \div \sqrt{ 18 }$$

Evaluate

$$\frac{\sqrt{6}}{2}\approx 1.224744871$$

Solution Steps

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

$$\frac{3\sqrt{2}\times \frac{1}{2}\sqrt{2}\sqrt{3}}{\sqrt{18}}$$

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

$$\frac{3\times 2\times \frac{1}{2}\sqrt{3}}{\sqrt{18}}$$

Multiply 3 and 2 to get 6.

$$\frac{6\times \frac{1}{2}\sqrt{3}}{\sqrt{18}}$$

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

$$\frac{\frac{6}{2}\sqrt{3}}{\sqrt{18}}$$

Divide 6 by 2 to get 3.

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

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

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

Cancel out 3 in both numerator and denominator.

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

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

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

The square of \sqrt{2} is 2.

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

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

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