Square Root of 1296
The square root of 1296 is also called root 1296 in short form. The square root of a number can be a rational/irrational number, positive/negative number, real/imaginary number. 1296 is a special number with its square root being a perfect square. Now we will see some cool facts about the square root of 1296 and few interesting problems as well.
 Square root of 1296: 36
 Square of 1296: 16,79,616
1.  What Is the Square Root of 1296? 
2.  Is Square Root of 1296 Rational or Irrational? 
3.  How to Find the Square Root of 1296? 
4.  Important Notes on Square Root of 1296 
5.  FAQs on Square Root of 1296 
What Is The Square Root of 1296?
 The square root of 1296 can be represented as √1296 and (1296)^{1/2}
 The square of 1296 will be a number(n) such that n × n = 1296
36 × 36 = 1296 also 36 × 36 = 1296
Therefore, +36 and 36 are the square roots of 1296.
Is Square Root of 1296 Rational or Irrational?
The square roots of 1296 are +36 and 36. Both numbers are integers and all integers are rational numbers. Therefore, the square root of 1296 is a rational number.
How to Find the Square Root of 1296?
Now we will find the square root of 1296 using the prime factorization and long division methods.
Square Root of 1296 by Prime Factorization Method
 Prime factorization of 1296: 2^{4} × 3^{4}
 Prime factors of 1296 in pairs: (2 × 2) × (2 × 2) × (3 × 3) × (3 × 3)
 Square root of 1296: √((2 × 2)^{2} × (3 × 3)^{2}) = (2)^{2 }× (3)^{2} = ±36
 Therefore, √1296 = ±36
Square Root of 1296 by Long Division Method
We will now find the square root of 1296 using the long division method:
 Start grouping the digits from the unit’s place in pairs of two by placing a bar on top of them. We have two pairs in this case, 12 and 96.
 Find a number(a) such that a × a ≤ 12. So, a will be 3 as 3 × 3 = 9 ≤ 12.
 We get the remainder and the quotient as 3. Also, add the divisor a with itself (3 + 3). We get the new divisor as 6.
 Bring down the next pair of numbers to form the new dividend. So, the new dividend is 396.
 Find a number(n) such that 6n × n ≤ 396. We get n = 6 as 66 × 6 = 396.
So, we get the square root of √1296 = 36 by the long division method.
Explore square roots using illustrations and interactive examples.
Important Notes:
 The number 1296 is a perfect square.
 The square root of 1296 is a rational number.
 The square root of 1296 is an imaginary number.
Square Root of 1296 Solved Examples

Example 1: Alex wants to know the value of √√1296. Can you help Alex find the answer?
Solution:
The square root of 1296 is √1296 = 36
Now the prime factorization of 36 = 2^{2} × 3^{2}
The square root 36 is (36)^{1/2} = ((2)^{2} × (3)^{2})^{1/2} = (2 × 3) = ±6. 
Example 2: Harper wants to find the average of the positive value of √1296 and √576. Can you help Harper find the value?
Solution:
The square root of 1296 is √1296 = 36
The square root of 476 is √576 = 24
The average of both numbers = (36 + 24)/2 = 60/2 = 30
FAQs on Square Root of 1296
What is the square root of 1296?
The square root of negative numbers is imaginary because squares of both positive and negative numbers result in positive numbers.
The square root of 1296 is represented as ±36i. (where i = √1)
What is the square of 1296?
Square of the number 1296 is (1296)^{2} = 16,79,616
What is the square root of 1296 in prime factorization form?
The square root of 1296 is √1296 = 36.
Now, the prime factorization of 36 = 2 × 2 × 3 × 3
Can we find the square root of 1296 using the approximation method?
No, we can’t find the square root of 1296 using the approximation method because the number 1296 is a perfect square and this method cannot be used in the case if the given number is a perfect square.
How is the square root of 1296 expressed in exponential and radical form?
 The square root of 1296 is written as (1296)^{1/2} in the exponential form.
 The square root of 1296 is written as √1296 in the radical form.
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