Solve sqrt{20}*5*1/2sqrt{3}

$$\sqrt { 20 } \times 5 \times 1 / 2 \sqrt { 3 }$$

Evaluate

$$5\sqrt{15}\approx 19.364916731$$

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}.

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

Multiply 5 and 2 to get 10.

$$10\sqrt{5}\times \frac{1}{2}\sqrt{3}$$

Multiply 10 and \frac{1}{2} to get \frac{10}{2}.

$$\frac{10}{2}\sqrt{5}\sqrt{3}$$

Divide 10 by 2 to get 5.

$$5\sqrt{5}\sqrt{3}$$

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

$$5\sqrt{15}$$