Square Root of 2625

The square root is the inverse of squaring a number. 2625 is not a perfect square. The square root of 2625 can be expressed in both radical and exponential form. In radical form, it is expressed as √2625, whereas in exponential form it is (2625)^(1/2). √2625 ≈ 51.23475, which is an irrational number because it cannot be expressed as a simple fraction p/q, where p and q are integers and q ≠ 0.

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 2625, methods such as 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 2625 is broken down into its prime factors:

Step 1: Finding the prime factors of 2625 Breaking it down, we get 5 x 5 x 3 x 3 x 29: 5^2 x 3^2 x 29

Step 2: Now that we have found the prime factors of 2625, the second step is to make pairs of those prime factors. Since 2625 is not a perfect square, it is impossible to pair all the digits of the number completely.

Therefore, calculating √2625 using prime factorization alone is not feasible.

The long division method is used for non-perfect square numbers. In this method, we find 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 2625, we need to group it as 25 and 26.

Step 2: Now, we need to find a number whose square is less than or equal to 26. We can say it is '5' because 5^2 = 25, which is less than or equal to 26. The quotient is 5, and after subtracting, 26 - 25, the remainder is 1.

Step 3: Bring down the next pair of digits (25), making the new dividend 125. Add the previous divisor (5) to itself to make the new divisor 10.

Step 4: Now, we need to find a digit that, when added to 10 and multiplied by the same digit, the product is less than or equal to 125. Let's choose 1. So, 101 x 1 = 101.

Step 5: Subtract 101 from 125, the difference is 24, and the quotient is 51.

Step 6: Since the new dividend is smaller than the new divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend, making it 2400.

Step 7: Find the new divisor, which is 102. Choose a digit, say 4, such that 1024 x 4 = 4096.

Step 8: Subtract 4096 from 2400, resulting in a negative number, so we need to adjust our choice. Choose 2 instead, so 1022 x 2 = 2044.

Step 9: Now, the remainder is 356, and the quotient becomes 51.2.

Step 10: Continue these steps until we get the desired precision.

The square root of √2625 ≈ 51.23475.

The approximation method is another way to find 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 2625 using the approximation method.

Step 1: Identify the closest perfect squares to √2625. The smallest perfect square less than 2625 is 2500, and the largest perfect square greater than 2625 is 2704. √2625 falls somewhere between 50 and 52.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (2625 - 2500) / (2704 - 2500) ≈ 0.125 Add this value to the square root of the nearest smaller perfect square: 50 + 0.125 = 50.125.

However, further refining through the long division method, we get √2625 ≈ 51.23475.

• Square root: A square root is the inverse operation of squaring a number. Example: 4² = 16, and the inverse of the square is the square root, that 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, the positive square root is more commonly used in practical applications. This is known as the principal square root.
   
• Prime factorization: Prime factorization is expressing a number as the product of its prime factors. For example, the prime factorization of 30 is 2 x 3 x 5.
   
• Long division method: The long division method is a process used to divide large numbers to find the square root or solve other division problems.