What is the square root of 27?

When simplifying a square root, I find that it is easiest to create a factor tree. A factor tree breaks down a number into it's prime factors. Prime numbers are whole numbers that only have factors of 1 and itself. Examples include 2, 3, 5, 7, 11, 13, 17, 19, 23 ... and so on.
You can break down sqrt(27)
into 3sqrt(3)
See the attached image to view the factor tree, which breaks down 27 into all of its prime factors.
For every pair of prime numbers that are part of the factor tree, you can take one outside of the radical.
For more information, please visit the following site:
https://socratic.org/questions/how-can-i-find-the-square-root-of-a-number-using-factor-trees

When evaluating a square root, you first determine between which 2 integers the square root falls using perfect squares. The square root of 27 is between the square root of 25 = 5 and the square root of 36 = 6. Then find the halfway point between the square root of 25 and 36 which is 30.5 and the halfway between 5 and 6 which is 5.5. Thus, the square root of 27 is between 5 and 5.5. 27 is slightly closer to 25 than 30.5 so 5.2 would be a good estimate. The square root of 26 would be approximately 5.1 whereas the square root of 28 would be approximately 5.3.

we can factorise 27 as
27=3x3x3
so sqrt(27)=sqrt(3x3x3)
=sqrt(3^2X3)
=3sqrt(3)
=3X1.732050757
=5.19615242271

There are two to three ways to answer your question.

Method 1- You can use a calculator and find the square root, it will be a decimal
Method 2- Approximation. If you only need an estimate, find numbers near 27 that have whole-number square roots. For 27, the numbers 25 and 36 are around 27 and have whole-number square roots (5 and 6). And since 27 is closer to 25 than 26, you can also estimate that your decimal answer should be closer to 5 than 6, and will likely even be under 5.5
Method 3- An exact answer. The answer above shows how to find an exact answer to the square root of 27. If you are having to find the square root of a larger number and are not sure what square numbers go into it, another option is to find the prime factorization of the number (breaking the number into all the smallest prime numbers that multiply to make it). For example, the prime factorization of 27 would be 3, 3, 3. The prime factorization of 30 would be 2, 3, 5. Any pairs of the same number can be re-written as that number squared. So 3x3x3 would be 3^2x3. And then taking the square root of any of those square numbers. So we would end up with a 3 on the outside of the square root and a 3 on the inside of the square root. The full math is shown below:
sqrt(27)=sqrt(3*3*3)=sqrt(3^2*3)=sqrt(3^2)*sqrt(3)=3sqrt(3)

Firstly we see that the number 27 is not a perfect square.Perfect square is a number we get by multiplying a number by itself,so that when we do its square root,we get the initial number itself.
But on other hand,27 can be written as
27=3×3×3
Further,
27=(3×3)×3
Two three to be taken as one as 27 is being square rooted,
Root of 27 can be written as 3×(root of 3)
.i.e 3×1.732=5.196(approx)

When simplifying a square root, we need to try to write the number as a product of a perfect square (e.g. 4, 9, 16, 25, 36 etc.) and some other number. In this case, 27 can be written as 9cdot3 so we have
sqrt27=sqrt(9cdot3)=sqrt9sqrt3=3sqrt3
Approximate decimal representation is easy to calculate on any calculator: sqrt27approx5.196152 . Of course, the same can be done by hand using logarithm tables, Babylonian method, or some similar numeric method. For more on that, check the links below.
https://en.wikipedia.org/wiki/Methods_of_computing_square_roots

https://en.wikipedia.org/wiki/Square_root