Square Root of 12544

The square root is the inverse of the square of a number. 12544 is a perfect square. The square root of 12544 is expressed in both radical and exponential form. In the radical form, it is expressed as √12544, whereas (12544)^(1/2) in the exponential form. √12544 = 112, 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. However, the prime factorization method is not used for non-perfect square numbers where long-division method and approximation method are used. Let us now learn the following methods:

1. Prime factorization method
2. Long division method
3. Approximation method

The product of prime factors is the prime factorization of a number. Now let us look at how 12544 is broken down into its prime factors.

Step 1: Finding the prime factors of 12544 Breaking it down, we get 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7: 2^6 × 7^2

Step 2: Now we found out the prime factors of 12544. The second step is to make pairs of those prime factors.

Since 12544 is a perfect square, we can group the digits into pairs: (2⁶ × 7²) = (2³ × 7)² = (8 × 7)² = 56². Therefore, the square root of 12544 using prime factorization is 56.

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

Step 1: To begin, we need to group the numbers from right to left. In the case of 12544, we need to group it as 44 and 125.

Step 2: Now, we need to find n whose square is closest to 125. We can say n is '11' because 11 × 11 = 121, which is less than 125. Now the quotient is 11, and after subtracting 121 from 125, the remainder is 4.

Step 3: Now, let us bring down 44 to make the new dividend 444.

Step 4: The new divisor will be the sum of the old divisor and the quotient doubled, which is 22.

Step 5: We now need to find a number that, when multiplied by (220 + n), is less than or equal to 444. This number is 2, as 222 × 2 = 444.

Step 6: Subtracting 444 from 444, the remainder is 0, and the quotient is 112. Therefore, the square root of 12544 is 112.

The approximation method is another method for finding square roots, and it can be used for both perfect and non-perfect squares. However, for perfect squares like 12544, the exact square root is preferred.

Step 1: Now we have to find the closest perfect square of √12544. 12544 is a perfect square, so the square root is exactly 112.

• Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, that is √16 = 4.

• Perfect square: A perfect square is a number that is the square of an integer. Example: 36 is a perfect square because it is 6².

• Rational number: A rational number is a number that can be expressed in the form of p/q, where p and q are integers and q is not equal to zero.

• Prime factorization: Prime factorization is the process of expressing a number as a product of its prime factors.

• Long division method: The long division method is a technique used to find the square root of a number by dividing and averaging.