Solve sqrt{1/3}+sqrt{27}-sqrt{(-2)^2}

$$\sqrt { \frac { 1 } { 3 } } + \sqrt { 27 } - \sqrt { ( - 2 ) ^ { 2 } }$$

Evaluate

$$\frac{10\sqrt{3}}{3}-2\approx 3.773502692$$

Solution Steps

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

$$\frac{\sqrt{1}}{\sqrt{3}}+\sqrt{27}-\sqrt{\left(-2\right)^{2}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{3}}+\sqrt{27}-\sqrt{\left(-2\right)^{2}}$$

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

$$\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\sqrt{27}-\sqrt{\left(-2\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{3}}{3}+\sqrt{27}-\sqrt{\left(-2\right)^{2}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

Combine \frac{\sqrt{3}}{3} and 3\sqrt{3} to get \frac{10}{3}\sqrt{3}.

$$\frac{10}{3}\sqrt{3}-\sqrt{\left(-2\right)^{2}}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{10}{3}\sqrt{3}-\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$\frac{10}{3}\sqrt{3}-2$$