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

$$2 \sqrt { 3 } - \frac { 1 } { 2 } \times \sqrt { 5 } \times \sqrt { 3 } \div \sqrt { 20 }$$

Evaluate

$$\frac{7\sqrt{3}}{4}\approx 3.031088913$$

Solution Steps

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

$$2\sqrt{3}-\frac{\frac{1}{2}\sqrt{15}}{\sqrt{20}}$$

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}.

$$2\sqrt{3}-\frac{\frac{1}{2}\sqrt{15}}{2\sqrt{5}}$$

Rationalize the denominator of \frac{\frac{1}{2}\sqrt{15}}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$2\sqrt{3}-\frac{\frac{1}{2}\sqrt{15}\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$2\sqrt{3}-\frac{\frac{1}{2}\sqrt{15}\sqrt{5}}{2\times 5}$$

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}.

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

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

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

Multiply 2 and 5 to get 10.

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

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

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

Divide \frac{5}{2}\sqrt{3} by 10 to get \frac{1}{4}\sqrt{3}.

$$2\sqrt{3}-\frac{1}{4}\sqrt{3}$$

Combine 2\sqrt{3} and -\frac{1}{4}\sqrt{3} to get \frac{7}{4}\sqrt{3}.

$$\frac{7}{4}\sqrt{3}$$