How do you find the square root of 81?
3 Answers
The square root of 81 is
Explanation:
The square root of 81 is
It is
Explanation:
Because the double multiplication for the same sign is always positive, the square root is also valid with the other sign
What if we do not know the value? There is an algorithm to calculate the square root quite simple (the Babylonian algorithm).
We want to calculate the square root of
Then the algorithm tell us that the next step of approximation is given by
I continue with the next approximation
As you can see in few steps the algorithm converges to the square root. Of course, because the previous discussion about the positive and negative sign, also the same result with the minus sign is a solution of the square root.
For me it is very fascinating the fact that I can write on Socratic.org, on Internet, an answer to someone that I do not know and that probably lives in a place that I will never see in my life, an algorithm to calculate the square root of a number invented 4000 years ago by some very clever Babylonian. Mathematics is the most universal language, trough space and time.
Explanation:
The square root of a number is that number which, when multiplied by itself will give the original number:
To find any root of a number, write the radicand as the product of its prime factors:
You can now understand this in different ways:

#sqrt81 = sqrt((3xx3)xx(3xx3)) = 3xx3 = 9# 
#sqrt81 = sqrt((3xx3)xx(3xx3)) = sqrt(9xx9) = 9# 
#sqrt81 = sqrt(3^4) = 3^(4div2) = 3^2 =9#
Note: