Use the pythagorean theorem to find the length of the missing side of a right triangle whose legs equal √2 and 2√15. a right triangle with legs as 2 square root of 15 and square root of 2.
a. 64
b. 4 + 2√15
c. 8
d. none of the above

The sides of a right triangle are called the 'legs' and the 'hypotenuse'.
Since you've given us the lengths of the 'legs', the missing side is the 'hypotenuse'

The square of the length of the hypotenuse is

         (square of the length of one leg) + (square of the length of the other leg).

                 Hypotenuse²  =  (√2)² + (2√15)²  = 

                                           (2)  +  (4 x 15)  =

                                            2   +    60       =  62.

                                                          Hypotenuse²    =  62

Take the square root of each side:        Hypotenuse = √62 =  7.874  (rounded)

None of the choices given is close enough.
It must be "none of the above".