Solve frac{sqrt{8}}{3}frac{sqrt{6}}{2}

$$\frac{ \sqrt{ 8 } }{ 3 } \frac{ \sqrt{ 6 } }{ 2 }$$

Evaluate

$$\frac{2\sqrt{3}}{3}\approx 1.154700538$$

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}.

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

Multiply \frac{2\sqrt{2}}{3} times \frac{\sqrt{6}}{2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2 in both numerator and denominator.

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

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}.

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

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

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