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.