The square root of 1296 is 36. If the given number is a multiple obtained by the product of the same number then the multiple is a perfect square. For example 1296 can be obtained by the product of the same number which is 36. ie 36 × 36 or – 36 × – 36 is 1296. Hence 1296 is a perfect square number and 36 its square root. There are many ways to find the square root of any given number, namely prime factorisation method, long division method, simplified method and repeated subtraction method. The square root of a number is represented as √1296 = 土36.
You can find the 1 to 50 Square and Square root List for reference.
Note the Following:
The Square root of 1296 = √1296 where √ = radical, and 1296 is the radicand.
Exponential Form of Square root of 1296 = 12961/2
Solution for √1296 = 36
Square root of 1296 is Irrational = False
What is the Square root of 1296?
The square root of 1296 is 36. In other words, the square of 36 is 1296. i.e 36 × 36 is 1296. Also – 36 × – 36 is 1296.
| √1296 = 36 |
How to Find the Square root of 1296?
There are three methods to find the Square root of 1296
- Prime Factorisation method
- Long Division method
- Repeated Subtraction method
Square root of 1296 by Prime Factorisation Method
The Square root of a number can be calculated only if the number is a perfect square number. 1296 is a perfect square number and it can be divided continuously by a prime number. Let us start with 3 as 1296 is not divisible by 2. Continue the division until the remainder becomes 1. The same prime divisors are grouped into 2 ( as this is square root) and the groups are multiplied to get the square root.
The given number, 1296 will be expressed as;
| 3 | 1296 |
| 3 | 432 |
| 3 | 144 |
| 3 | 48 |
| 2 | 16 |
| 2 | 8 |
| 2 | 4 |
| 2 | 2 |
| × | 1 |
1296 = 3 × 3 × 3 × 3 × 2 × 2 × 2 × 2
Grouping into 2 with same divisors:
Group 1 = 3 × 3, considering only 3
Group 2 = 3 × 3, considering only 3
Group 3 = 2 × 2, considering only 2
Group 3 = 2 × 2, considering only 2
Therefore the square root of 1296 = 3 × 3 × 2 × 2 = 36.
Square root of 1296 by Long Division Method
To understand the long division method, follow the below mentioned detailed steps;
Step 1: Â Grouping the given number into pairs
Given number is 1296, grouping it as 12 and 96.
| 12 96 |
Step 2: Consider the first number, which is 12.
Let us find a square number that divides 12
i.e
1 × 1 = 1
2 × 2 = 4
3 × 3 = 9
4 × 4 = 16
5 × 5 = 25
The square number that is to be considered for dividing 12 will be 3 x 3.
Step 3: Dividing 12 by 3
Step 4: Continue the division using the next number 96
The first number to be used as the next divisor is 3 + 3 = 6 (Divisor of first division + quotient of first division)
Now considering a two digit number starting with 6 to divide 396 will be
61 × 1 = 61
62 × 2 = 124
63 × 3 = 189
64 × 4 = 256
65 × 5 = 325
66 × 6 = 396
Continue the division as
Since the Division is complete with remainder as zero, the quotient becomes the square root of the given number.
Therefore the Square root of 1296 is 36.
Square root of 1296 by Repeated Subtraction Method.
For finding the square root of 1296 using the repeated subtraction method, 1296 is first subtracted by 1, the resultant by 3, the next resultant by 5 and so on. The subtraction is stopped when the resultant becomes zero. The step at which the result becomes zero, forms the square root of 1296. Let us find the result in the table below.
For the given number 1296, steps for repeated subtraction are
| Step 1 | 1296 | – | 1 | = | 1295 |
| Step 2 | 1295 | – | 3 | = | 1292 |
| Step 3 | 1292 | – | 5 | = | 1287 |
| Step 4 | 1287 | – | 7 | = | 1280 |
| Step 5 | 1280 | – | 9 | = | 1271 |
| Step 6 | 1271 | – | 11 | = | 1260 |
| Step 7 | 1260 | – | 13 | = | 1247 |
| Step 8 | 1247 | – | 15 | = | 1232 |
| Step 9 | 1232 | – | 17 | = | 1215 |
| Step 10 | 1215 | – | 19 | = | 1196 |
| Step 11 | 1196 | – | 21 | = | 1175 |
| Step 12 | 1175 | – | 23 | = | 1152 |
| Step 13 | 1152 | – | 25 | = | 1127 |
| Step 14 | 1127 | – | 27 | = | 1100 |
| Step 15 | 1100 | – | 29 | = | 1071 |
| Step 16 | 1071 | – | 31 | = | 1040 |
| Step 17 | 1040 | – | 33 | = | 1007 |
| Step 18 | 1007 | – | 35 | = | 972 |
| Step 19 | 972 | – | 37 | = | 935 |
| Step 20 | 935 | – | 39 | = | 896 |
| Step 21 | 896 | – | 41 | = | 855 |
| Step 22 | 855 | – | 43 | = | 812 |
| Step 23 | 812 | – | 45 | = | 767 |
| Step 24 | 767 | – | 47 | = | 720 |
| Step 25 | 720 | – | 49 | = | 671 |
| Step 26 | 671 | – | 51 | = | 620 |
| Step 27 | 620 | – | 53 | = | 567 |
| Step 28 | 567 | – | 55 | = | 512 |
| Step 29 | 512 | – | 57 | = | 455 |
| Step 30 | 455 | – | 59 | = | 396 |
| Step 31 | 396 | – | 61 | = | 335 |
| Step 32 | 335 | – | 63 | = | 272 |
| Step 33 | 272 | – | 65 | = | 207 |
| Step 34 | 207 | – | 67 | = | 140 |
| Step 35 | 140 | – | 69 | = | 71 |
| Step 36 | 71 | – | 71 | = | 0 |
Since the result of zero is obtained in the 36th Step, the square root of 1296 is 36.
Video Lessons
Visualising square roots
Finding Square roots
Related Articles
- Square Root
- What is Square root?
- Finding Square roots
- Squares and Square roots
- Finding Square root with Example
- Square root Calculator
Solved Examples
1. What is the square root of 12?
12 does not have a perfect square root. The approximate value of square root of 12 is 3.46.
2. What is the square root of 100?
10 is the square root of 100.
Comments