Square Root of 2500

The square root is the inverse of the square of the number. 2500 is a perfect square. The square root of 2500 is expressed in both radical and exponential form. In the radical form, it is expressed as √2500, whereas (2500)^(1/2) in the exponential form. √2500 = 50, 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 often used for perfect square numbers. However, the prime factorization method can also be verified using the long division method to ensure accuracy. Let us now learn the following methods:

• Prime factorization method
• Long division method

The product of prime factors is the prime factorization of a number. Now let us look at how 2500 is broken down into its prime factors.

Step 1: Finding the prime factors of 2500 Breaking it down, we get 2 x 2 x 5 x 5 x 5 x 5: 2^2 x 5^4

Step 2: Now we found out the prime factors of 2500. The second step is to make pairs of those prime factors. Since 2500 is a perfect square, we can group the digits in pairs.

The square root of 2500 using prime factorization is 2 x 5 x 5 = 50.

The long division method is used to verify the square root of 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 2500, we need to group it as 25 and 00.

Step 2: Now we need to find n whose square is 25. We can say n is '5' because 5 x 5 is equal to 25. Now the quotient is 5, and after subtracting 25-25, the remainder is 0.

Step 3: Now let us bring down 00, which is the new dividend. Add the old divisor with the same number 5 + 5, we 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, we need to find the value of n.

Step 5: The next step is finding 10n x n ≤ 00. Let us consider n as 0, now 10 x 0 x 0 = 0.

Step 6: Subtracting 00 from 0, the difference is 0, and the quotient is 50.

Step 7: Since there are no remaining digits, the square root of 2500 is confirmed as 50.

The approximation method is not necessary for perfect squares but can be useful for non-perfect squares. However, knowing the process is beneficial. For perfect squares like 2500, the exact value is known.

Step 1: Recognize 2500 is a perfect square. The closest perfect square is 2500 itself.

Step 2: Since 2500 is 50 x 50, we have the exact value.

Thus, the square root of 2500 is 50.

• Square root: A square root is the inverse of a square. Example: 50² = 2500 and the inverse of the square is the square root, that is, √2500 = 50.
   
• Perfect square: A perfect square is a number that is the square of an integer. For example, 2500 is a perfect square because it is 50 squared.
   
• 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.
   
• Principal square root: A number has both positive and negative square roots, but it is always the positive square root that has more prominence due to its uses in the real world. That is why it is also known as the principal square root.
   
• Long division method: A mathematical method used to divide large numbers and also used to find square roots of numbers, especially to approximate non-perfect squares.