Solve sqrt{(2-9)^2+(5-12)^2}

$$\sqrt { ( 2 - 9 ) ^ { 2 } + ( 5 - 12 ) ^ { 2 } }$$

Evaluate

$$7\sqrt{2}\approx 9.899494937$$

Solution Steps

Subtract 9 from 2 to get -7.

$$\sqrt{\left(-7\right)^{2}+\left(5-12\right)^{2}}$$

Calculate -7 to the power of 2 and get 49.

$$\sqrt{49+\left(5-12\right)^{2}}$$

Subtract 12 from 5 to get -7.

$$\sqrt{49+\left(-7\right)^{2}}$$

Calculate -7 to the power of 2 and get 49.

$$\sqrt{49+49}$$

Add 49 and 49 to get 98.

$$\sqrt{98}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$7\sqrt{2}$$