Question

How do you find the square root of \[189\]?

Answer 1

Hint:
In the above question we are given a number that is \[189\] which is a real number and we are asked to depict the method of finding the square root of this given number. So while approaching such questions one should know about the square root of the expression as the square root of an expression is the number which when squared produces the same expression. Now let us see the method to find the square root of the given number in the question that is \[189\] in the complete step by step solution.

Complete step by step solution:
Here we are given a term that is \[189\] and we are asked the method of its square root.
So firstly by seeing the given number we can say that it is a real numbers (the numbers which we use in the general terms and it is also positive) and we are asked to find the square root also which means we need to find that number which when squared or multiplied with itself twice gives the number that is given to us and asked a square root for it. So the square root of the given term \[189\] is done as-
As we can see from the given number in the question that it is not a perfect square so the square of it would be found by breaking the given number into its factors that is depicted as –
\[
  \sqrt[{}]{{189}} \\
  \sqrt[{}]{{3{\times}3{\times}21}} \\
 \]
Now using the property of the numbers under the square root that is –
\[\sqrt {ab} = \sqrt a \sqrt b \] (it can be used only if the condition is satisfied that is \[ab \geqslant 0\] which means both the numbers multiplying under the square root is greater than \[0\] or in simpler terms they are given positive to us
So using the above property we get-
\[
  \sqrt 9 \sqrt {21} \\
   = 3\sqrt {21} \\
 \] as the square root of the \[9\] is \[3\]
So the cube root of the number \[189\] is \[ = 3\sqrt {21} \]

Hence the required answer for the square root of \[189\] is \[ = 3\sqrt {21} \]

Note:
While solving this kind of question one should know about the square root of the numbers, the perfect square numbers identification of these numbers and the solving of the imperfect square numbers and the utter concentration while solving these questions is required which would lead to the precision in the solution and getting the right answer also.