Question

What is the square root of 12.5?

Answer 1

Hint: To find the square root of $12.5$ , we are going to use the method of log. First of all, let the square root of $12.5$ be x. Now, square root can also be denoted by raising the number by ${\displaystyle \frac{1}{2}}$ .So, we will get the equation as $x={\left(12.5\right)}^{{\displaystyle \frac{1}{2}}}$ .Now, take log on both sides and then simplify RHS. After that, to find the value of x, take antilog on both sides and we will get our answer.

Complete step-by-step answer:
In this question, we are supposed to find the square root of 12.5.
We can easily find this using a calculator, but we are going to see a method to find the square root of any number without using a calculator.
For this, we are going to use the log method.
First of all, the square root of a number means the number which when multiplied two times will give the original number. Square root of a number is denoted by $\sqrt{}$ .
Let the square root of $12.5$ be $x$ .
 $\Rightarrow x=\sqrt{12.5}$
We can also write square roots as raised to ${\displaystyle \frac{1}{2}}$ .
 $\Rightarrow x={\left(12.5\right)}^{{\displaystyle \frac{1}{2}}}$ - - - - - - (1)
Now, to find the square root of a number using log method, introduce log on both sides of the equation.
Therefore, equation (1) becomes
 $\Rightarrow \log x=\log {\left(12.5\right)}^{{\displaystyle \frac{1}{2}}}$ - - - - - - - - (2)
Now, we have the property $\log a^b=b\log a$ . Therefore, equation (2) becomes
 $\Rightarrow \log x={\displaystyle \frac{1}{2}}\log \left(12.5\right)$ - - - - - - - (3)
Now, the value of $\log 12.5=1.0969$ . Therefore, equation (3) becomes
 $\Rightarrow \log x={\displaystyle \frac{1}{2}}\left(1.0969\right)$
 $\Rightarrow \log x=0.548455$
Now, we need the value of x. So, take antilog on both sides, we get
 $$\begin{gathered} \Rightarrow x=anti\log \left(0.548455\right) \\ \Rightarrow x=\text{3}\text{.535534} \end{gathered}$$
Hence, the square root of $12.5$ is $$\text{3}\text{.535534}$$.
So, the correct answer is “$$\text{3}\text{.535534}$$”.

Note: Square root of a number is written under $\sqrt{}$ sign and this sign is called a radical sign. The value inside this sign is called radical.