Solve sqrt{1/2}*sqrt{18}

$$\sqrt { \frac { 1 } { 2 } } \times \sqrt { 18 }$$

Evaluate

$$3$$

Solution Steps

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

$$\frac{\sqrt{1}}{\sqrt{2}}\sqrt{18}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{2}}\sqrt{18}$$

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

$$\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\sqrt{18}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{2}\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

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

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

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

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

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

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

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

Cancel out 2 and 2.

$$3$$

Factor

$$3$$