Question

What is the geometric mean of $32$ and $2$?

Answer 1

To solve this question we need to know about the geometric mean. Geometric mean of two numbers is the square root of the product of the two numbers so if we consider the two numbers as “a” and “b” then the geometric mean will be the square root of the product of “a” and “b”. To solve, we will firstly find the product of the two numbers and then will find the square root of the product.

Complete step-by-step solution:
The question asks us to find the geometric mean of the two numbers, where the two numbers given are $32$ and $2$. To start with the calculation we will firstly know about the geometric mean of the two numbers. So basically the square root of the product of the numbers will be the geometric mean. Firstly will find out the product of the two numbers therefore on multiplying the two numbers we get:
$\Rightarrow 32\times 2$
$\Rightarrow 64$
The second step will be to find the square root of the product. On doing so we get:
$\Rightarrow GM=\sqrt{64}$
$64$ is the square of $8$. So we will substitute $64$with ${{8}^{2}}$, on doing this we get:
$\Rightarrow GM=\sqrt{{{8}^{2}}}$
$\Rightarrow GM=8$
$\therefore$ The geometric mean of $32$ and $2$is $8$.
Note: When we are asked to find the Geometric Mean of “n” number then the formula used to find the geometric mean will be $\dfrac{1}{{{n}^{th}}}$ power of the product of the “n” numbers. Example: If we are asked to find the geometric mean of ${{a}_{1}},{{a}_{2}},{{a}_{3}}...........{{a}_{n}}$, then the geometric mean of the numbers will be $\sqrt[n]{{{a}_{1}}\times {{a}_{2}}\times {{a}_{3}}...........{{a}_{n}}}$ .