Solve alpha=sqrt{(6-9)^2+(7-1)^2}

$$\alpha = \sqrt { ( 6 - 9 ) ^ { 2 } + ( 7 - 1 ) ^ { 2 } }$$

Solve for α

$$\alpha =3\sqrt{5}\approx 6.708203932$$

Steps for Solving Linear Equation

Subtract 9 from 6 to get -3.

$$\alpha =\sqrt{\left(-3\right)^{2}+\left(7-1\right)^{2}}$$

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

$$\alpha =\sqrt{9+\left(7-1\right)^{2}}$$

Subtract 1 from 7 to get 6.

$$\alpha =\sqrt{9+6^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\alpha =\sqrt{9+36}$$

Add 9 and 36 to get 45.

$$\alpha =\sqrt{45}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$\alpha =3\sqrt{5}$$

Assign α

$$\alpha ≔3\sqrt{5}$$