Find the hypotenuse of each isosceles right triangle when the legs are of the given measure. Given = 8"

there is no option for radical 128

Use the Pythagorean Theorem:  c²  =  a² + b²

a  and  b  represent the lengths of the legs; so,  a = 8  and  b = 8  (since the triangle is isosceles)

--->   c²  =  8² + b²   --->   c²  =  64 + 64   --->   c²  =  128   --->   c  =  √128

$$\\\sqrt{128}=\sqrt{4*32}\\
=\sqrt{4*16*2}\\
=\sqrt{4}\sqrt{16}\sqrt{2}\\
=2*4*\sqrt{2}\\
=8\sqrt{2}$$