Solve sqrt{15}divsqrt{12}*sqrt{3/2}

$$\sqrt { 15 } \div \sqrt { 12 } \times \sqrt { \frac { 3 } { 2 } }$$

Evaluate

$$\frac{\sqrt{30}}{4}\approx 1.369306394$$

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}.

$$\frac{\sqrt{15}}{2\sqrt{3}}\sqrt{\frac{3}{2}}$$

Rationalize the denominator of \frac{\sqrt{15}}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{\sqrt{15}\sqrt{3}}{2\times 3}\sqrt{\frac{3}{2}}$$

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

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

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

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

Multiply 2 and 3 to get 6.

$$\frac{3\sqrt{5}}{6}\sqrt{\frac{3}{2}}$$

Divide 3\sqrt{5} by 6 to get \frac{1}{2}\sqrt{5}.

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

Rewrite the square root of the division \sqrt{\frac{3}{2}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2}}.

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

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

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

The square of \sqrt{2} is 2.

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

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{1}{2}\sqrt{5}\times \frac{\sqrt{6}}{2}$$

Multiply \frac{1}{2} times \frac{\sqrt{6}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{6}}{2\times 2}\sqrt{5}$$

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{6}}{4}\sqrt{5}$$

Express \frac{\sqrt{6}}{4}\sqrt{5} as a single fraction.

$$\frac{\sqrt{6}\sqrt{5}}{4}$$

To multiply \sqrt{6} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{30}}{4}$$