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

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

Evaluate

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

Solution Steps

Add -6 and 11 to get 5.

$$\sqrt{5^{2}+\left(9-14\right)^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{25+\left(9-14\right)^{2}}$$

Subtract 14 from 9 to get -5.

$$\sqrt{25+\left(-5\right)^{2}}$$

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

$$\sqrt{25+25}$$

Add 25 and 25 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}.

$$5\sqrt{2}$$