Solve sqrt{(14-4)^2+(-11+6)^2}+(9-10)^2

$$\sqrt { ( 14 - 4 ) ^ { 2 } + ( - 11 + 6 ) ^ { 2 } } + ( 9 - 10 ) ^ { 2 }$$

Evaluate

$$5\sqrt{5}+1\approx 12.180339887$$

Solution Steps

Subtract 4 from 14 to get 10.

$$\sqrt{10^{2}+\left(-11+6\right)^{2}}+\left(9-10\right)^{2}$$

Calculate 10 to the power of 2 and get 100.

$$\sqrt{100+\left(-11+6\right)^{2}}+\left(9-10\right)^{2}$$

Add -11 and 6 to get -5.

$$\sqrt{100+\left(-5\right)^{2}}+\left(9-10\right)^{2}$$

Calculate -5 to the power of 2 and get 25.

$$\sqrt{100+25}+\left(9-10\right)^{2}$$

Add 100 and 25 to get 125.

$$\sqrt{125}+\left(9-10\right)^{2}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$5\sqrt{5}+\left(9-10\right)^{2}$$

Subtract 10 from 9 to get -1.

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

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

$$5\sqrt{5}+1$$