Square Root of 2600

The square root is the inverse of the square of the number. 2600 is not a perfect square. The square root of 2600 is expressed in both radical and exponential form. In the radical form, it is expressed as √2600, whereas (2600)^(1/2) in the exponential form. √2600 = 50.9902, 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 2600 is broken down into its prime factors:

Step 1: Finding the prime factors of 2600 Breaking it down, we get 2 x 2 x 2 x 5 x 5 x 13: 2^3 x 5^2 x 13

Step 2: Now we found out the prime factors of 2600. The second step is to make pairs of those prime factors. Since 2600 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.

Therefore, calculating 2600 using prime factorization is not straightforward for an exact square root.

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 2600, we need to group it as 26 and 00.

Step 2: Now we need to find n whose square is less than or equal to 26. We can say n is ‘5’ because 5 x 5 is 25, which is less than 26. Now the quotient is 5 and the remainder is 1.

Step 3: Now let us bring down 00, making the new dividend 100. 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: The next step is finding 10n × n ≤ 100. Let us consider n as 0, now 10 x 0 x 0 = 0.

Step 6: Subtract 100 from 0; the difference is 100, and the quotient is 50.

Step 7: Since the new dividend is more than the divisor, we need to bring down another pair of zeros. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 10000.

Step 8: Now we need to find the new divisor, which is 509, because 509 x 9 = 4581.

Step 9: Subtracting 4581 from 10000, we get the result 5419.

Step 10: Now the quotient is 50.9.

Step 11: Continue doing these steps until we get two numbers after the decimal point, or until the remainder is zero.

So the square root of √2600 is approximately 50.99.

The approximation method is another method for finding the 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 2600 using the approximation method.

Step 1: Now we have to find the closest perfect squares around √2600. The smallest perfect square less than 2600 is 2500, and the largest perfect square greater than 2600 is 2704. √2600 falls between 50 (for √2500) and 52 (for √2704).

Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (2600 - 2500) ÷ (2704 - 2500) = 100 ÷ 204 ≈ 0.49. Using the formula, we identified the decimal point of our square root. The next step is adding the base value to the decimal number, which is 50 + 0.49 = 50.49.

Thus, the square root of 2600 is approximately 50.99.

• 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; however, it is usually the positive square root that has more prominence due to its uses in the real world. This is known as the principal square root.
   
• Long division method: A method used to find the square root of non-perfect squares by dividing the number into pairs and solving step-by-step.
   
• Approximation method: A method used to find the square root of non-perfect squares by estimating the value between known perfect squares and using a formula to find a more accurate result.