Solve 3sqrt{1/3}-6sqrt{1/2}

$$3 \sqrt { \frac { 1 } { 3 } } - 6 \sqrt { \frac { 1 } { 2 } }$$

Evaluate

$$\sqrt{3}-3\sqrt{2}\approx -2.51058988$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

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

Calculate the square root of 1 and get 1.

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

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

$$3\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-6\sqrt{\frac{1}{2}}$$

The square of \sqrt{3} is 3.

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

Cancel out 3 and 3.

$$\sqrt{3}-6\sqrt{\frac{1}{2}}$$

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

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

Calculate the square root of 1 and get 1.

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

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

$$\sqrt{3}-6\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\sqrt{3}-6\times \frac{\sqrt{2}}{2}$$

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

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

Factor

$$\sqrt{3} - 3 \sqrt{2} = -2.51058988$$