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

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

Evaluate

$$2\sqrt{13}\approx 7.211102551$$

Solution Steps

The opposite of -2 is 2.

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

Add 4 and 2 to get 6.

$$\sqrt{6^{2}+\left(0-4\right)^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\sqrt{36+\left(0-4\right)^{2}}$$

Subtract 4 from 0 to get -4.

$$\sqrt{36+\left(-4\right)^{2}}$$

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

$$\sqrt{36+16}$$

Add 36 and 16 to get 52.

$$\sqrt{52}$$

Factor 52=2^{2}\times 13. Rewrite the square root of the product \sqrt{2^{2}\times 13} as the product of square roots \sqrt{2^{2}}\sqrt{13}. Take the square root of 2^{2}.

$$2\sqrt{13}$$