Solve sqrt{left(-5-4right)^2+left(-6+3right)^2}

$$\sqrt{ { \left(-5-4 \right) }^{ 2 } + { \left(-6+3 \right) }^{ 2 } }$$

Evaluate

$$3\sqrt{10}\approx 9.486832981$$

Solution Steps

Subtract 4 from -5 to get -9.

$$\sqrt{\left(-9\right)^{2}+\left(-6+3\right)^{2}}$$

Calculate -9 to the power of 2 and get 81.

$$\sqrt{81+\left(-6+3\right)^{2}}$$

Add -6 and 3 to get -3.

$$\sqrt{81+\left(-3\right)^{2}}$$

Calculate -3 to the power of 2 and get 9.

$$\sqrt{81+9}$$

Add 81 and 9 to get 90.

$$\sqrt{90}$$

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

$$3\sqrt{10}$$