Respuesta :
Answer:
Exact distance: [tex]\sqrt{139}[/tex] units.
Approximate distance: 11.8 units.
Step-by-step explanation:
We have been given two points [tex](4\sqrt{3},\sqrt{7})[/tex] and [tex](\sqrt{3},5\sqrt{7})[/tex]. We are asked to find the distance between the given points.
We will use distance formula to solve our given problem.
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]D=\sqrt{(4\sqrt{3}-\sqrt{3})^2+(5\sqrt{7}-\sqrt{7})^2}[/tex]
[tex]D=\sqrt{(3\sqrt{3})^2+(4\sqrt{7})^2}[/tex]
[tex]D=\sqrt{9\cdot 3+16\cdot 7}[/tex]
[tex]D=\sqrt{27+112}[/tex]
[tex]D=\sqrt{139}[/tex]
Therefore, the distance between the given points is [tex]\sqrt{139}[/tex] units.
The approximate distance between the given points is [tex]\sqrt{139}=11.7898\approx 11.8[/tex] units.
