Solve sqrt{left(-10-2right)^2+left(-5-1right)^2}

$$\sqrt{ { \left(-10-2 \right) }^{ 2 } + { \left(-5-1 \right) }^{ 2 } }$$

Evaluate

$$6\sqrt{5}\approx 13.416407865$$

Solution Steps

Subtract 2 from -10 to get -12.

$$\sqrt{\left(-12\right)^{2}+\left(-5-1\right)^{2}}$$

Calculate -12 to the power of 2 and get 144.

$$\sqrt{144+\left(-5-1\right)^{2}}$$

Subtract 1 from -5 to get -6.

$$\sqrt{144+\left(-6\right)^{2}}$$

Calculate -6 to the power of 2 and get 36.

$$\sqrt{144+36}$$

Add 144 and 36 to get 180.

$$\sqrt{180}$$

Factor 180=6^{2}\times 5. Rewrite the square root of the product \sqrt{6^{2}\times 5} as the product of square roots \sqrt{6^{2}}\sqrt{5}. Take the square root of 6^{2}.

$$6\sqrt{5}$$