Final answer:
The distance between the points (-5,4) and (-1,8) is calculated using the distance formula and the result is expressed in simplest radical form as 4√2.
Step-by-step explanation:
To find the distance between the two points (-5,4) and (-1,8) in simplest radical form, we use the distance formula derived from the Pythagorean theorem:
Distance = √((x2 - x1)² + (y2 - y1)²)
Plugging in the given points:
Distance = √((-1 - (-5))² + (8 - 4)²)
= √((4)² + (4)²)
= √(16 + 16)
= √(32)
To express √(32) in simplest radical form, we find the prime factors of 32 which are 2×5, and simplify:
Distance = √(16 × 2)
= √(16) × √(2)
= 4√2
Therefore, the distance between the points in simplest radical form is 4√2.