Question

what is the geometric mean of 3 and 7?

Answer 1

\(\bf \cfrac{3}{{\color{red}{ x}}}=\cfrac{{\color{red}{ x}}}{7}\)

Answer 2

so is it just 3*7?

Answer 3

well.. what did you get?

Answer 4

if you cross-multiply... what do you end up with?

Answer 5

\(\bf \cfrac{3}{{\color{red}{ x}}}=\cfrac{{\color{red}{ x}}}{7}\implies 3\cdot 7={\color{red}{ x\cdot x}}\implies 21=x^2\\ \quad \\
\textit{taking square root to both sides}\\ \quad \\
\sqrt{21}=\sqrt{x^2}\implies \sqrt{21}=x\)