Solve sqrt{left(-2--4right)^2+left(-5-3right)^2}

$$\sqrt{ { \left(-2--4 \right) }^{ 2 } + { \left(-5-3 \right) }^{ 2 } }$$

Evaluate

$$2\sqrt{17}\approx 8.246211251$$

Solution Steps

The opposite of -4 is 4.

$$\sqrt{\left(-2+4\right)^{2}+\left(-5-3\right)^{2}}$$

Add -2 and 4 to get 2.

$$\sqrt{2^{2}+\left(-5-3\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{4+\left(-5-3\right)^{2}}$$

Subtract 3 from -5 to get -8.

$$\sqrt{4+\left(-8\right)^{2}}$$

Calculate -8 to the power of 2 and get 64.

$$\sqrt{4+64}$$

Add 4 and 64 to get 68.

$$\sqrt{68}$$

Factor 68=2^{2}\times 17. Rewrite the square root of the product \sqrt{2^{2}\times 17} as the product of square roots \sqrt{2^{2}}\sqrt{17}. Take the square root of 2^{2}.

$$2\sqrt{17}$$