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

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

Evaluate

$$2\sqrt{3}\approx 3.464101615$$

Solution Steps

Subtract 1 from -2 to get -3.

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

Calculate -3 to the power of 2 and get 9.

$$\sqrt{9+\left(2\sqrt{3}-\sqrt{3}\right)^{2}}$$

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

$$\sqrt{9+\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{9+3}$$

Add 9 and 3 to get 12.

$$\sqrt{12}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$2\sqrt{3}$$