Solve sqrt{15}*frac{sqrt{20}}{4}

$$\sqrt { 15 } \times \frac { \sqrt { 20 } } { 4 }$$

Evaluate

$$\frac{5\sqrt{3}}{2}\approx 4.330127019$$

Solution Steps

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}.

$$\sqrt{15}\times \frac{2\sqrt{5}}{4}$$

Divide 2\sqrt{5} by 4 to get \frac{1}{2}\sqrt{5}.

$$\sqrt{15}\times \frac{1}{2}\sqrt{5}$$

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

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

Multiply \sqrt{5} and \sqrt{5} to get 5.

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

Multiply 5 and \frac{1}{2} to get \frac{5}{2}.

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