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 $ \dfrac{1}{2} $ .So, we will get the equation as $ x = {\left( {12.5} \right)^{\dfrac{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 $ \dfrac{1}{2} $ .
 $ \Rightarrow x = {\left( {12.5} \right)^{\dfrac{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)^{\dfrac{1}{2}}} $ - - - - - - - - (2)
Now, we have the property $ \log {a^b} = b\log a $ . Therefore, equation (2) becomes
 $ \Rightarrow \log x = \dfrac{1}{2}\log \left( {12.5} \right) $ - - - - - - - (3)
Now, the value of $ \log 12.5 = 1.0969 $ . Therefore, equation (3) becomes
 $ \Rightarrow \log x = \dfrac{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
 $
   \Rightarrow x = anti\log \left( {0.548455} \right) \\
   \Rightarrow x = {\text{3}}{\text{.535534}} \;
  $
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.