Solve frac{sqrt{2}*sqrt{24}}{sqrt{8}}

$$\frac { \sqrt { 2 } \times \sqrt { 24 } } { \sqrt { 8 } }$$

Evaluate

$$\sqrt{6}\approx 2.449489743$$

Solution Steps

Factor 24=2\times 12. Rewrite the square root of the product \sqrt{2\times 12} as the product of square roots \sqrt{2}\sqrt{12}.

$$\frac{\sqrt{2}\sqrt{2}\sqrt{12}}{\sqrt{8}}$$

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

$$\frac{2\sqrt{12}}{\sqrt{8}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{2\times 2\sqrt{3}}{\sqrt{8}}$$

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{3}}{\sqrt{8}}$$

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}.

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

Cancel out 2 in both numerator and denominator.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Cancel out 2 and 2.

$$\sqrt{6}$$