Square Root of 2900

The square root is the inverse of the square of the number. 2900 is not a perfect square. The square root of 2900 is expressed in both radical and exponential forms. In the radical form, it is expressed as √2900, whereas (2900)^(1/2) in the exponential form. The square root of 2900 is approximately 53.851648, 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 2900 is broken down into its prime factors:

Step 1: Finding the prime factors of 2900 Breaking it down, we get 2 x 2 x 5 x 5 x 29: 2^2 x 5^2 x 29

Step 2: Now we found out the prime factors of 2900. The second step is to make pairs of those prime factors. Since 2900 is not a perfect square, therefore the digits of the number can’t be grouped into pairs completely. Therefore, calculating the square root of 2900 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 2900, we need to group it as 29 and 00.

Step 2: Now we need to find n whose square is less than or equal to 29. We can say n as ‘5’ because 5 × 5 = 25, which is less than 29. Now the quotient is 5, and after subtracting 29 - 25, the remainder is 4.

Step 3: Now let us bring down 00, which is the new dividend. 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 the 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 × n ≤ 400. Let us consider n as 3, now 10 × 3 × 3 = 90

Step 6: Subtract 400 from 90, the difference is 310, and the quotient is 53

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 31000.

Step 8: Now we need to find the new divisor that is 107 because 1077 × 7 = 7539

Step 9: Subtracting 7539 from 31000 we get the result 23461.

Step 10: Now the quotient is 53.8

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.

So the square root of √2900 is approximately 53.85

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 2900 using the approximation method.

Step 1: Now we have to find the closest perfect square of √2900. The smallest perfect square less than 2900 is 2809 (which is 53^2), and the largest perfect square is 2916 (which is 54^2). √2900 falls somewhere between 53 and 54.

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 (2900 - 2809) ÷ (2916 - 2809) = 91 ÷ 107 = 0.850467 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 53 + 0.850467 = 53.850467, so the square root of 2900 is approximately 53.85.

• Square root: A square root is the inverse of a square. For example, 4^2 = 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 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.
   
• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 2900 is 2^2 x 5^2 x 29.
   
• Long division method: A technique used to find the square root of non-perfect squares by breaking down the number into a series of steps to approximate the square root.