Question

Evaluate the square root of 5?

Answer 1

Hint: To find the square root of 5, we are going to use the method of log. First of all, let the square root of 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( 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 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 5 be $ x $ .
 $ \Rightarrow x = \sqrt 5 $
We can also write square roots as raised to $ \dfrac{1}{2} $ .
 $ \Rightarrow x = {\left( 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( 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( 5 \right) $ - - - - - - - (3)
Now, the value of $ \log 5 = 0.69897 $ . Therefore, equation (3) becomes
 $ \Rightarrow \log x = \dfrac{1}{2}\left( {0.69897} \right) $
 $ \Rightarrow \log x = 0.3494850022 $
Now, we need the value of x. So, take antilog on both sides, we get
 $
   \Rightarrow x = anti\log \left( {0.3494850022} \right) \\
   \Rightarrow x = 2.23606 \;
  $
Hence, the square root of 5 is 2.23606.
So, the correct answer is “Option B”.

Note: Here, we can cross check our answer by multiplying 2.23606 two times.
 $ \to 2.23606 \times 2.23606 = 4.9999821 $
Hence, our answer is correct.