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

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

Evaluate

$$-2\sqrt{2}\approx -2.828427125$$

Solution Steps

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2 and 2.

$$\sqrt{2}-\sqrt{18}$$

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}.

$$\sqrt{2}-3\sqrt{2}$$

Combine \sqrt{2} and -3\sqrt{2} to get -2\sqrt{2}.

$$-2\sqrt{2}$$