Square Root of 2520

The square root is the inverse of the square of the number. 2520 is not a perfect square. The square root of 2520 is expressed in both radical and exponential form. In the radical form, it is expressed as √2520, whereas (2520)^(1/2) in the exponential form. √2520 ≈ 50.199, 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 2520 is broken down into its prime factors:

Step 1: Finding the prime factors of 2520 Breaking it down, we get 2 × 2 × 2 × 3 × 3 × 5 × 7: 2^3 × 3^2 × 5 × 7

Step 2: Now we found out the prime factors of 2520. The second step is to make pairs of those prime factors. Since 2520 is not a perfect square, the digits of the number can’t be grouped in pairs completely.

Therefore, calculating √2520 using prime factorization requires approximations and simplifications.

The long division method is particularly used for non-perfect square numbers. In this method, we 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 2520, we need to group it as 20 and 25.

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

Step 3: Now let us bring down 20, 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 × n ≤ 20. Let us consider n as 2, now 10 × 2 × 2 = 40, which is not possible, so we need to find a smaller n.

Step 6: Subtract 20 from 10, the difference is 10, and the quotient is 50.

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 1000.

Step 8: Now we need to find the new divisor that is 1005 because 1005 × 1 = 1005, which is not possible. We need to adjust n and divisor to fit.

Step 9: Subtracting is adjusted to find an appropriate value, resulting in a more precise decimal.

Step 10: Now the quotient is approximately 50.2

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

So the square root of √2520 is approximately 50.2.

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 2520 using the approximation method.

Step 1: Now we have to find the closest perfect square of √2520. The smallest perfect square less than 2520 is 2500 (since 50^2 = 2500) and the largest perfect square greater than 2520 is 2601 (since 51^2 = 2601). √2520 falls somewhere between 50 and 51.

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 (2520 - 2500) ÷ (2601 - 2500) = 20 ÷ 101 ≈ 0.198. 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 + 0.2 ≈ 50.2.

So the square root of 2520 is approximately 50.2.

• Square root: A square root is the inverse of a square. 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.
   
• Perfect square: A perfect square is a number that is the square of an integer. Example: 49 is a perfect square because 7 × 7 = 49.
   
• Decimal: If a number has a whole number and a fraction in a single number then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
   
• Prime factorization: Prime factorization is writing a number as a product of its prime factors. Example: 30 can be written as 2 × 3 × 5.