Solve sqrt{left(1-2right)^2+left(7-0right)^2}

$$\sqrt{ { \left(1-2 \right) }^{ 2 } + { \left(7-0 \right) }^{ 2 } }$$

Evaluate

$$5\sqrt{2}\approx 7.071067812$$

Solution Steps

Subtract 2 from 1 to get -1.

$$\sqrt{\left(-1\right)^{2}+\left(7-0\right)^{2}}$$

Calculate -1 to the power of 2 and get 1.

$$\sqrt{1+\left(7-0\right)^{2}}$$

Subtract 0 from 7 to get 7.

$$\sqrt{1+7^{2}}$$

Calculate 7 to the power of 2 and get 49.

$$\sqrt{1+49}$$

Add 1 and 49 to get 50.

$$\sqrt{50}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$5\sqrt{2}$$