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.

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

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.

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.

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.

• 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.