Question

What is the square root of $0.9$?

Answer 1

Hint: To find the square root of $0.9$, we are going to use the method of log. First of all, let the square root of $0.9$ be x. Now, square root can also be denoted by raising the number by $\dfrac{1}{2}$.So, we will get the equation as $x = {\left( {0.9} \right)^{\dfrac{1}{2}}}$.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 solution:
In this question we have to find the square root of $0.9$. Now, we can find its square root using the long division method or using the log method. But the long division method will be a little complicated so 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 gives the original number. Square root is denoted by $\sqrt {} $.
Let the square root of $0.9$ be x.
$ \Rightarrow x = \sqrt {0.9} $
We can write square roots as raised to $\dfrac{1}{2}$ also.
$ \Rightarrow x = {\left( {0.9} \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( {0.9} \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( {0.9} \right)$- - - - - - - - - (3)
Now, the value of $\log 0.9 = - 0.045757$. Therefore, above equation becomes
$ \Rightarrow \log x = - \dfrac{1}{2}\left( {0.045757} \right)$
$ \Rightarrow \log x = - 0.0228787$
Now, we need the value of x. So, take antilog on both sides, we get
$
   \Rightarrow x = anti\log \left( { - 0.0228787} \right) \\
   \Rightarrow x = {\text{0}}{\text{.9486834}} \\
 $.
Hence, the square root of $0.9$ is \[{\text{0}}{\text{.9486834}}\].

Note: Here, we can verify our answer by multiplying our answer two times.
${\text{0}}{\text{.9486834}} \times {\text{0}}{\text{.9486834}} = 0.9000000193$.
Hence, our answer is correct. We can find any root of a given number using the log method.