Question

What is the perfect square of the square root of \[185\]?

Answer 1

Hint: Square root of a number is a value, which on multiplied by itself gives the original number. Suppose, ‘x’ is the square root of ‘y’, then it is represented as \[x = \sqrt y \] or we can express the same equation as \[{x^2} = y\]. Here we can see that 185 is not a perfect square.

Complete step by step solution:
Given, perfect square of the square root of \[185\]
That is \[{\left( {\sqrt {185} } \right)^2} = 185\]. This is the required answer.
Because square and square root will get canceled.
Suppose if they asked us to find the square root of 185 then,
185 can be factorized as 5 and 37. It will not give us the desired result.
We use a calculator to get the results. That is
\[ \Rightarrow \sqrt {185} = 13.601\]
So, the correct answer is “185”.

Note: Here \[\sqrt {} \] is the radical symbol used to represent the root of numbers. The number under the radical symbol is called radicand. The positive number, when multiplied by itself, represents the square of the number. The square root of the square of a positive number gives the original number. To find the factors, find the smallest prime number that divides the given number and divide it by that number, and then again find the smallest prime number that divides the number obtained and so on. The set of prime numbers obtained that are multiplied to each other to form the bigger number are called the factors.