Solve sqrt{10}*sqrt{3}div2sqrt{10}divsqrt{3}=

$$\sqrt { 10 } \times \sqrt { 3 } \div 2 \sqrt { 10 } \div \sqrt { 3 } =$$

Evaluate

$$5$$

Solution Steps

To multiply \sqrt{10} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\frac{\sqrt{30}}{2}\sqrt{10}}{\sqrt{3}}$$

Express \frac{\sqrt{30}}{2}\sqrt{10} as a single fraction.

$$\frac{\frac{\sqrt{30}\sqrt{10}}{2}}{\sqrt{3}}$$

Express \frac{\frac{\sqrt{30}\sqrt{10}}{2}}{\sqrt{3}} as a single fraction.

$$\frac{\sqrt{30}\sqrt{10}}{2\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{30}\sqrt{10}}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{30}\sqrt{10}\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{30}\sqrt{10}\sqrt{3}}{2\times 3}$$

Factor 30=10\times 3. Rewrite the square root of the product \sqrt{10\times 3} as the product of square roots \sqrt{10}\sqrt{3}.

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

Multiply \sqrt{10} and \sqrt{10} to get 10.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{10\times 3}{2\times 3}$$

Multiply 10 and 3 to get 30.

$$\frac{30}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{30}{6}$$

Divide 30 by 6 to get 5.

$$5$$

Factor

$$5$$