Solve sqrt{6}*sqrt{8}divsqrt{2}

$$\sqrt { 6 } \cdot \sqrt { 8 } \div \sqrt { 2 }$$

Evaluate

$$2\sqrt{6}\approx 4.898979486$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

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}.

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

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

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

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

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

The square of \sqrt{2} is 2.

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

Multiply 2 and 2 to get 4.

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

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

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

Divide 4\sqrt{6} by 2 to get 2\sqrt{6}.

$$2\sqrt{6}$$