Question

What is the geometric mean of 4 and 16?
A). 2
B). 4
C). 6
D). 8

Answer 1

Hint: We are given two numbers. We know that if a and b are the two numbers then the geometric mean is given by the root of the product of the two given numbers such that \[\sqrt {ab} \] will be the geometric mean of the two numbers a and b. Now we will apply the same with the two numbers given above.

Complete step-by-step solution:
Given that the two numbers are 4 and 16.
Now the product of 4 and 16 is 64.
The geometric mean is given by the root of the product of the two numbers.
So the geometric mean of 4 and 16 will be the root of 64.
And we know that 64 is the perfect square of 8. So \[\sqrt {64} = 8\]
Thus 8 is the geometric mean of 4 and 16.
So option D is the correct option.

Note: We also know the concept of geometric progression. If a, b and c are in a G.P. such that the ratio between the consecutive terms is constant then the geometric mean is given by,
\[b = \sqrt {ac} \]
Thus we used the same for the above only the thing is we found the mean here.