The geometric mean of two numbers is the square root of their product. In you instance any two factors of 900 will have a geometric mean of 30
eg 2 & 450 (2 x 15 = 30, 30 x 15 = 450);
3 & 300 (3 x 10 = 30, 30 x 10 = 300);
6 & 150 (6 x 5 = 30, 30 x 5 = 150) etc etc
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The geometric mean is the square root of the product of two numbers. In this case, sqrt(24*30) = sqrt(720) =~ 26.8 A method for number lovers: 24=8x3=23x31. 30=6x5=21x31x51. 720 = 23+1x31+1x51 = 24x32x5 sqrt(720) = sqrt(24)xsqrt(32)xsqrt(5) = 22x31xsqrt5 = 12sqrt5 (=~12x2.236 =~ 26.8)
2*15 = 30 are one pair amongst others2*15 or 1*30
√3 x √300 = 1.73205080756888 x 17.3205080756888 = 30