Question

find the distance between the pair of points. ( square root 5, square root 2) and -3 square root 5, 5 square root 2)

Answer 1

Use the distance formula 

d  = sqrt ((y2-y1)^2  + (x2-x1)^2))

    =   sqrt ( (5 sqrt2 - sqrt2)^2  +  ( -3sqrt5 - sqrt5)^2)
  
   =     sqrt [( 4sqrt2)^2 + (4sqrt5)^2]

   = sqrt   (32 +  16*5)  =  sqrt 112  = sqrt16 * sqrt7  = 4 sqrt7

The answer is  4 sqrt7