Square Root of 12600

The square root is the inverse of the square of the number. 12600 is not a perfect square. The square root of 12600 is expressed in both radical and exponential form. In the radical form, it is expressed as √12600, whereas (12600)^(1/2) in the exponential form. √12600 ≈ 112.245, which is an irrational number because it cannot 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 the 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 12600 is broken down into its prime factors.

Step 1: Finding the prime factors of 12600 Breaking it down, we get 2 x 2 x 2 x 3 x 3 x 5 x 5 x 7: 2^3 x 3^2 x 5^2 x 7

Step 2: Now we found out the prime factors of 12600. The second step is to make pairs of those prime factors. Since 12600 is not a perfect square, therefore the digits of the number can’t be grouped in pairs entirely.

Therefore, calculating the square root of 12600 using prime factorization is not straightforward.

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. 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 12600, we need to group it as 12, 60, and 0.

Step 2: Now we need to find n whose square is less than or equal to 12. We can say n as '3' because 3 x 3 = 9 is less than 12. Now the quotient is 3, after subtracting 12 - 9, the remainder is 3.

Step 3: Now let us bring down 60, making the new dividend 360. Add the old divisor with the same number (3 + 3) to get 6, which will be our new divisor.

Step 4: The new divisor is 60n, and we need to find the value of n such that 60n x n ≤ 360. Let us consider n as 6, now 60 x 6 = 360.

Step 5: Subtracting 360 from 360 gives a remainder of 0, and the quotient is 36. Step 6: Since the remainder is 0, we can stop here. The square root of 12600 is approximately 112.245.

The approximation method is another method for finding square roots, and it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 12600 using the approximation method.

Step 1: Now we have to find the closest perfect square to √12600. The smallest perfect square less than 12600 is 12100 (111²), and the largest perfect square greater than 12600 is 12996 (114²). √12600 falls somewhere between 110 and 114.

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).

Using the formula (12600 - 12100) / (12996 - 12100) ≈ 0.5 Using the formula, we identified the decimal point of our square root.

The next step is adding the value we got initially to the decimal number which is 110 + 0.5 = 110.5, so the square root of 12600 is approximately 112.245.

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

• Irrational Number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.

• Principal Square Root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.

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

• Long Division Method: The long division method is a technique for dividing larger numbers into simpler steps, often used to find square roots of non-perfect squares.