Square Root of 2501

The square root is the inverse of the square of the number. 2501 is not a perfect square. The square root of 2501 is expressed in both radical and exponential form. In the radical form, it is expressed as √2501, whereas (2501)^(1/2) in the exponential form. √2501 ≈ 50.009999, 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 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 2501 is broken down into its prime factors.

Step 1: Finding the prime factors of 2501 Breaking it down, we get 41 x 61.

Step 2: Now we found out the prime factors of 2501. The second step is to make pairs of those prime factors. Since 2501 is not a perfect square, calculating 2501 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 2501, we need to group it as 01 and 25.

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

Step 3: Now let us bring down 01, making the new dividend 01. 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 10n. We need to find the value of n such that 10n x n ≤ 01. Here, since the dividend is smaller than the divisor, we add a decimal point to the quotient and bring down two zeros to the dividend, making it 100.

Step 5: The next step is finding 100n x n ≤ 100. Let's consider n as 0, since 100 x 0 = 0.

Step 6: Subtracting 0 from 100, the difference is 100, and the quotient is 50.0.

Step 7: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.

So the square root of √2501 ≈ 50.01.

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 2501 using the approximation method.

Step 1: Now we have to find the closest perfect square of √2501. The smallest perfect square less than 2501 is 2500, and the largest perfect square greater than 2501 is 2601. √2501 falls somewhere between 50 and 51.

Step 2: Now we need to apply the formula (Given number - smallest perfect square) / (Next perfect square - smallest perfect square). Using the formula (2501 - 2500) / (2601 - 2500) = 1/101 ≈ 0.0099. 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 + 0.0099 ≈ 50.01.

So the square root of 2501 is approximately 50.01.

• Square root: A square root is the inverse of a square. For 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, but the positive square root is often more useful in practical applications. This is known as the principal square root.
   
• Decimal: If a number has a whole number and a fraction in a single number, it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.
   
• Long division method: A systematic method used to find the square root of numbers that are not perfect squares, involving dividing the number into groups and finding roots step by step.