There are two methods on how to work out such a problem:

__Method 1__1. Multiply the two numbers (8 * 25 = 200). 2.Calculate the square root of this number (√200 = 14.14213562)__Method 2__The geometric mean can be solved, algebraically speaking, by using the following equation: First #/x = x/Second # 8/x = x/25 (plug in the values) x^2 = 200 (Cross multiply: X * x = x^2 and 8 * 25 = 200) √x^2 = √200 (eliminate the exponent) x = 14.14213562 ______ Final Answer:The geometric mean of 8 and 25 is 14.14213562