Square Root of 2628

The square root is the inverse of the square of the number. 2628 is not a perfect square. The square root of 2628 is expressed in both radical and exponential forms. In the radical form, it is expressed as √2628, whereas in the exponential form it is (2628)^(1/2). √2628 ≈ 51.264, 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:

• 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 2628 is broken down into its prime factors.

Step 1: Finding the prime factors of 2628 Breaking it down, we get 2 x 2 x 3 x 3 x 73: 2² x 3² x 73

Step 2: Now we found out the prime factors of 2628. Since 2628 is not a perfect square, the digits of the number can’t be grouped in pairs.

Therefore, calculating 2628 using prime factorization is not straightforward.

The long division method is particularly used for non-perfect square numbers. In this method, we 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 2628, we need to group it as 28 and 26.

Step 2: Now find n whose square is less than or equal to 26. We can say n = 5 because 5 x 5 is 25, which is less than or equal to 26. Now the quotient is 5, and after subtracting 25 from 26, the remainder is 1.

Step 3: Bring down 28, making the new dividend 128. Add the old divisor with the same number 5 + 5 to get 10, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 10n as the new divisor, and we need to find the value of n.

Step 5: Find 10n x n ≤ 128. Let us consider n as 1, now 101 x 1 = 101.

Step 6: Subtract 101 from 128, and the difference is 27.

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 2700.

Step 8: Find the new divisor that is 102, because 1022 x 2 = 2044.

Step 9: Subtracting 2044 from 2700, we get the result 656.

Step 10: Now the quotient is 51.2.

Step 11: Continue doing these steps until we get the desired decimal places.

So the square root of √2628 ≈ 51.264

The approximation method is another method for finding square roots; 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 2628 using the approximation method.

Step 1: Find the closest perfect squares to √2628. The smallest perfect square less than 2628 is 2500, and the largest perfect square greater than 2628 is 2704. √2628 falls between 50 and 52.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula, (2628 - 2500) / (2704 - 2500) = 0.514 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 50 + 0.514 ≈ 51.264.

So the square root of 2628 is approximately 51.264

• Square root: A square root is the inverse of squaring a number. Example: 4² = 16, and the inverse operation is √16 = 4.
   
• Irrational number: An irrational number is a number that cannot be written in the form 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, the positive square root is often used in real-world applications and is thus known as the principal square root.
   
• Approximation: An approximation is a value or number that is close to the exact value but not exactly equal. It is often used for non-perfect squares.
   
• Long division method: This is a method for finding the square root of non-perfect squares, involving a step-by-step division process to obtain an approximate value.