Solve sqrt{(-4-10)^2+(-3-5)^2}

$$\sqrt { ( - 4 - 10 ) ^ { 2 } + ( - 3 - 5 ) ^ { 2 } }$$

Evaluate

$$2\sqrt{65}\approx 16.124515497$$

Solution Steps

Subtract 10 from -4 to get -14.

$$\sqrt{\left(-14\right)^{2}+\left(-3-5\right)^{2}}$$

Calculate -14 to the power of 2 and get 196.

$$\sqrt{196+\left(-3-5\right)^{2}}$$

Subtract 5 from -3 to get -8.

$$\sqrt{196+\left(-8\right)^{2}}$$

Calculate -8 to the power of 2 and get 64.

$$\sqrt{196+64}$$

Add 196 and 64 to get 260.

$$\sqrt{260}$$

Factor 260=2^{2}\times 65. Rewrite the square root of the product \sqrt{2^{2}\times 65} as the product of square roots \sqrt{2^{2}}\sqrt{65}. Take the square root of 2^{2}.

$$2\sqrt{65}$$