Solve =sqrt{(-1-3)^2+(4-0)^2}

$$= \sqrt { ( - 1 - 3 ) ^ { 2 } + ( 4 - 0 ) ^ { 2 } }$$

Evaluate

$$4\sqrt{2}\approx 5.656854249$$

Solution Steps

Subtract 3 from -1 to get -4.

$$\sqrt{\left(-4\right)^{2}+\left(4-0\right)^{2}}$$

Calculate -4 to the power of 2 and get 16.

$$\sqrt{16+\left(4-0\right)^{2}}$$

Subtract 0 from 4 to get 4.

$$\sqrt{16+4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{16+16}$$

Add 16 and 16 to get 32.

$$\sqrt{32}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$4\sqrt{2}$$