Solve sqrt{left(6-8right)^2+left(8-6right)^2}

$$\sqrt{ { \left(6-8 \right) }^{ 2 } + { \left(8-6 \right) }^{ 2 } }$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

Subtract 8 from 6 to get -2.

$$\sqrt{\left(-2\right)^{2}+\left(8-6\right)^{2}}$$

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

$$\sqrt{4+\left(8-6\right)^{2}}$$

Subtract 6 from 8 to get 2.

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

Calculate 2 to the power of 2 and get 4.

$$\sqrt{4+4}$$

Add 4 and 4 to get 8.

$$\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{2}$$