Solve sqrt{left(9-1right)^2+left(1-5right)^2}

$$\sqrt{ { \left(9-1 \right) }^{ 2 } + { \left(1-5 \right) }^{ 2 } }$$

Evaluate

$$4\sqrt{5}\approx 8.94427191$$

Solution Steps

Subtract 1 from 9 to get 8.

$$\sqrt{8^{2}+\left(1-5\right)^{2}}$$

Calculate 8 to the power of 2 and get 64.

$$\sqrt{64+\left(1-5\right)^{2}}$$

Subtract 5 from 1 to get -4.

$$\sqrt{64+\left(-4\right)^{2}}$$

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

$$\sqrt{64+16}$$

Add 64 and 16 to get 80.

$$\sqrt{80}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$4\sqrt{5}$$