Solve sqrt{left(2+1right)^2+left(0-3right)^2}

$$\sqrt{ { \left(2+1 \right) }^{ 2 } + { \left(0-3 \right) }^{ 2 } }$$

Evaluate

$$3\sqrt{2}\approx 4.242640687$$

Solution Steps

Add 2 and 1 to get 3.

$$\sqrt{3^{2}+\left(0-3\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{9+\left(0-3\right)^{2}}$$

Subtract 3 from 0 to get -3.

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

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

$$\sqrt{9+9}$$

Add 9 and 9 to get 18.

$$\sqrt{18}$$

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}.

$$3\sqrt{2}$$