Solve 2sqrt{1/18}

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

Evaluate

$$\frac{\sqrt{2}}{3}\approx 0.471404521$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{18}} as the division of square roots \frac{\sqrt{1}}{\sqrt{18}}.

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

Calculate the square root of 1 and get 1.

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

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}.

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

Rationalize the denominator of \frac{1}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Multiply 3 and 2 to get 6.

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

Cancel out 6, the greatest common factor in 2 and 6.

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