Square root of 36
How would you find the side length of a square if the area in square inches is given. The answer is finding square root of the given area. Suppose if the area of square is given as 36 square inches. What could be its side length?
To answer this question let us learn how to find the square root of 36.
 Square Root of 36: √36 = 6
 Square of 36: 36^{2} = 1296
1.  What Is the Square Root of 36? 
2.  Is Square Root of 36 Rational or Irrational? 
3.  How to Find the Square Root of 36? 
4.  FAQs on Square Root of 36 
What Is the Square Root of 36?
The square root of a number is a number whose square gives the original number. For example, to find the square root of 36 (which is denoted by √36), we have to think of a number whose square is 36
You can remember it this way: When the square moves from one side to the other side of the equation, it becomes the square root.
 6^{2} = 36
 √36 = 6
Thus, the square root of 36 is 6.
Is the Square Root of 36 Rational or Irrational?
A rational number can be expressed as a fraction of integers. We already found that
 √36 = 6 = 6/1
So we could express √36 as a fraction of integers and hence it is a rational number.
 √36 is a rational number.
How to Find the Square Root of 36?
We can find the square root of 36 using various methods.
 Repeated Subtraction
 Prime Factorization
 Estimation and Approximation
 Long Division
If you want to learn more about each of these methods, click here.
We know that 36 is a perfect square, so we can find its square root using the prime factorization method easily.
Square Root of 36 Using Prime Factorization
The prime factorization of 36 is as follows:
 36 is: 36 = 2 × 2 × 3 × 3
To find the square root of 36, we take one number from each pair of the same numbers and multiply them.
 √36 = 2 × 3 = 6
Square Root of 36 By Long Division
The square root of 36 can be found using the long division as follows.
Think of a number which when multiplied by itself gives
 a number that is less than or equal to 36
 a number that is very close to 36
Since the remainder is 0, we do not need to proceed with long division further and we consider the quotient (which is 6) as the result.
 √36 = 6
Explore square roots using illustrations and interactive examples.
Think Tank:
 Can the value of √36 be 6 as well?
Hint: Think what is (6)^{2}  Is √36 a real number?
Hint: Think whether there is any real number whose square is negative.
Important Notes:
 If we do not have pairs of the same numbers as above, then the prime factorization cannot be used to find the exact square root. Instead, we have to use the long division method.
 The prime factorization method is used to write a square root of a nonperfect square number in the simplest radical form.
For example:
18 = 2 × 3 × 3 = 2 × 3^{2}
So, √18 = √2 × √3^{2} = 3√2
Square Root of 36 Solved Examples

Example 1
Jack is instructed to find the square root of 36 using the laws of exponents. Can we help him with this?
Solution
The square root can be always replaced with the exponent 1/2.
√36 = 36^{½}
= (6^{2})^{½}Since 6^{2} = 36 = 6 [(a^{m})^{n} = a^{mn}]
Thus, √36 = 6 
Example 2
There are as many seats in a minivan as the number of rows in it. If there are 36 seats in it, then how many rows are there?
Solution
Let us assume the number of seats in the minivan is y.
By the given information,
y×y = 36
y^{2} = 36
By taking the square root on both sides,
√y^{2} = √36
We know that the square root of y^{2} is y.
Also, we know that 6^{2} = 36 and so the square root of 36 is 6
y= 6The number of rows = 6
FAQs On Square Root of 36
What is the square root of 36?
As we learned on this page, the square root of 36 can be either 6 or 6.
What is the square of 36?
The square of 36 is 1296.
36^{2} = 1296
How do you work out the square root of 36?
We can find the square root of 36 using various methods.
 Repeated Subtraction
 Prime Factorization
 Estimation and Approximation
 Long Division
If you want to learn more about each of these methods, click here.
How do you find a square root?
We can find the square root using various methods.
 Repeated Subtraction
 Prime Factorization
 Estimation and Approximation
 Long Division
If you want to learn more about each of these methods, click here.
What is the square root of 36 in the simplest radical form?
√36 is the simplest radical form.
Is the square root of 36 a rational number?
√36 = 6= 6/1.
√36 is a rational number.