Question

If 'x' is the geometric mean of 6a³b and 6ab³, then find the value of X.​

Answer 1

Geometric mean is given by -

$\sf \: GM = \sqrt{n_1 n_2}$

Now,

$\sf \: x = \sqrt{(6 {a}^{3} b)(6a {b}^{3})} \\ \\ \implies \sf \: x = \sqrt{36 {a}^{4}b {}^{4} } \\ \\ \implies \boxed{ \boxed{ \sf \: x = 6 {a}^{2} {b}^{2} }}$