Question

Find the geometric mean of square root of 28 and square root of 7.

Answer 1

Geometric mean of two numbers a and b is given as
\[\large GM=\sqrt{ab}\]
here \(a= \sqrt {28}\) and \(b= \sqrt 7\)
so
\[GM=\sqrt {\sqrt{28} \times \sqrt {7}}\]
We have now
\[\large GM=\sqrt {\sqrt{196}}\]
or
\[\large GM =\sqrt{14}\]
The GM is
\[\huge \sqrt {14}\]