Find three numbers in the ratio 2:3:5, the sum of whose squares is 608.

Let the three numbers a, b, c, be 2x, 3x, 5x.

we know that

(2x) ^2 + (3x) ^2 + (5x) ^2 = 608

4x^2 + 9x^2 + 25x^2 = 608

38x^2 = 608

x^2 = 608/38

x^2=16

x = √16

x = 4

a = 2x = 2*4=8

b=3x = 3*4=12

c = 5x = 5*4=20

the three numbers are 8,12,20