Solve 2sqrt{12}*1/4div5sqrt{2}

$$2 \sqrt { 12 } \times \frac { 1 } { 4 } \div 5 \sqrt { 2 }$$

Evaluate

$$\frac{\sqrt{6}}{5}\approx 0.489897949$$

Solution Steps

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}.

$$\frac{2\times 2\sqrt{3}\times \frac{1}{4}}{5}\sqrt{2}$$

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{3}\times \frac{1}{4}}{5}\sqrt{2}$$

Cancel out 4 and 4.

$$\frac{\sqrt{3}}{5}\sqrt{2}$$

Express \frac{\sqrt{3}}{5}\sqrt{2} as a single fraction.

$$\frac{\sqrt{3}\sqrt{2}}{5}$$

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

$$\frac{\sqrt{6}}{5}$$