Solve frac{sqrt{5}*sqrt{12}}{sqrt{20}}

$$\frac { \sqrt { 5 } \cdot \sqrt { 12 } } { \sqrt { 20 } }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

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}.

$$\frac{\sqrt{5}\times 2\sqrt{3}}{\sqrt{20}}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{15}\times 2}{\sqrt{20}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{\sqrt{15}\times 2}{2\sqrt{5}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\sqrt{15}}{\sqrt{5}}$$

Rewrite the division of square roots \frac{\sqrt{15}}{\sqrt{5}} as the square root of the division \sqrt{\frac{15}{5}} and perform the division.

$$\sqrt{3}$$