Solve d=sqrt{((-4)-3)^2+(3-4)^2}

$$d = \sqrt { ( ( - 4 ) - 3 ) ^ { 2 } + ( 3 - 4 ) ^ { 2 } }$$

Solve for d

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

Steps for Solving Linear Equation

Subtract 3 from -4 to get -7.

$$d=\sqrt{\left(-7\right)^{2}+\left(3-4\right)^{2}}$$

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

$$d=\sqrt{49+\left(3-4\right)^{2}}$$

Subtract 4 from 3 to get -1.

$$d=\sqrt{49+\left(-1\right)^{2}}$$

Calculate -1 to the power of 2 and get 1.

$$d=\sqrt{49+1}$$

Add 49 and 1 to get 50.

$$d=\sqrt{50}$$

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}.

$$d=5\sqrt{2}$$

Assign d

$$d≔5\sqrt{2}$$