Solve 3sqrt{1/2}*5sqrt{6}

$$3 \sqrt{ \frac{ 1 }{ 2 } } \times 5 \sqrt{ 6 }$$

Evaluate

$$15\sqrt{3}\approx 25.980762114$$

Solution Steps

Multiply 3 and 5 to get 15.

$$15\sqrt{\frac{1}{2}}\sqrt{6}$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$15\times \frac{\sqrt{1}}{\sqrt{2}}\sqrt{6}$$

Calculate the square root of 1 and get 1.

$$15\times \frac{1}{\sqrt{2}}\sqrt{6}$$

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

$$15\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\sqrt{6}$$

The square of \sqrt{2} is 2.

$$15\times \frac{\sqrt{2}}{2}\sqrt{6}$$

Express 15\times \frac{\sqrt{2}}{2} as a single fraction.

$$\frac{15\sqrt{2}}{2}\sqrt{6}$$

Express \frac{15\sqrt{2}}{2}\sqrt{6} as a single fraction.

$$\frac{15\sqrt{2}\sqrt{6}}{2}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 15 and 2 to get 30.

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

Divide 30\sqrt{3} by 2 to get 15\sqrt{3}.

$$15\sqrt{3}$$