Square Root of 1296
2026-02-28 15:47 Diff
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Last updated on August 5, 2025

If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 1296.

What is the Square Root of 1296?

The square root is the inverse of the square of the number. 1296 is a perfect square. The square root of 1296 can be expressed in both radical and exponential form. In radical form, it is expressed as √1296, whereas (1296)^(1/2) in exponential form. √1296 = 36, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 1296

The prime factorization method is used for perfect square numbers. For non-perfect square numbers, the long division method and approximation method are used. Let us now learn the following methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 1296 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 1296 is broken down into its prime factors.

Step 1: Finding the prime factors of 1296

Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3: 2^4 x 3^4

Step 2: Now we found out the prime factors of 1296. Since 1296 is a perfect square, we can pair the prime factors. Therefore, √1296 = (2^2 x 3^2) = 36.

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Square Root of 1296 by Long Division Method

The long division method is particularly used for non-perfect square numbers, but it can also verify perfect squares. Let us now learn how to find the square root using the long division method, step by step.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 1296, we group it as 12 and 96.

Step 2: Now we need to find n whose square is less than or equal to 12. We can say n is ‘3’ because 3 x 3 = 9, which is less than 12. The quotient is 3, and the remainder is 12 - 9 = 3.

Step 3: Now bring down 96, making the new dividend 396. Double the quotient (3) to get 6, which becomes part of our new divisor.

Step 4: Find a digit x such that 6x x x is less than or equal to 396. Here, x is 6, because 66 x 6 = 396.

Step 5: Subtract 396 from 396 to get a remainder of 0. The quotient is 36, which is the square root of 1296.

Square Root of 1296 by Approximation Method

The approximation method is another method for finding square roots, especially for non-perfect squares. It is not necessary for perfect square 1296, but let's apply it for understanding.

Step 1: We have to find the closest perfect squares around √1296. Since 1296 is a perfect square, it's exactly 36.

Step 2: Using the approximation method is unnecessary here, as the perfect square of 1296 is exactly 36.

Common Mistakes and How to Avoid Them in the Square Root of 1296

Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division steps, etc. Now let us look at a few of those mistakes that students tend to make in detail.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √169?

Okay, lets begin

The area of the square is 169 square units.

Explanation

The area of the square = side^2.

The side length is given as √169.

Area of the square = side^2 = √169 x √169 = 13 x 13 = 169.

Therefore, the area of the square box is 169 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 1296 square feet is built; if each of the sides is √1296, what will be the square feet of half of the building?

Okay, lets begin

648 square feet

Explanation

We can just divide the given area by 2 as the building is square-shaped.

Dividing 1296 by 2, we get 648.

So half of the building measures 648 square feet.

Well explained 👍

Problem 3

Calculate √1296 x 5.

Okay, lets begin

180

Explanation

The first step is to find the square root of 1296, which is 36.

The second step is to multiply 36 by 5.

So, 36 x 5 = 180.

Well explained 👍

Problem 4

What will be the square root of (144 + 9)?

Okay, lets begin

The square root is 12.

Explanation

To find the square root, we need to find the sum of (144 + 9). 144 + 9 = 153, and then √153 cannot be simplified as a perfect square.

Therefore, the square root of (144 + 9) is approximately 12.37 (for simplicity, the nearest integer is 12).

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √256 units and the width ‘w’ is 40 units.

Okay, lets begin

We find the perimeter of the rectangle as 96 units.

Explanation

Perimeter of the rectangle = 2 × (length + width).

Perimeter = 2 × (√256 + 40) = 2 × (16 + 40) = 2 × 56 = 112 units.

Well explained 👍

FAQ on Square Root of 1296

1.What is √1296 in its simplest form?

The prime factorization of 1296 is 2^4 x 3^4, so the simplest form of √1296 = √(2^4 x 3^4) = 36.

2.Mention the factors of 1296.

Factors of 1296 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648, and 1296.

3.Calculate the square of 1296.

We get the square of 1296 by multiplying the number by itself, that is 1296 x 1296 = 1,679,616.

4.Is 1296 a prime number?

1296 is not a prime number, as it has more than two factors.

5.1296 is divisible by?

1296 has many factors; those are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648, and 1296.

Important Glossaries for the Square Root of 1296

  • Square root: A square root is the inverse of a square. Example: 6^2 = 36 and the inverse of the square is the square root, which is √36 = 6.
  • Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.
  • Perfect square: A perfect square is an integer that is the square of an integer. For example, 36 is a perfect square because it is 6^2.
  • Dividend: In division, the number that is being divided is called the dividend. For example, in 1296 ÷ 36 = 36, 1296 is the dividend.
  • Divisor: In division, the number by which the dividend is divided is called the divisor. For example, in 1296 ÷ 36 = 36, 36 is the divisor.

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.