Square Root of 2420

The square root is the inverse of the square of the number. 2420 is not a perfect square. The square root of 2420 is expressed in both radical and exponential form. In the radical form, it is expressed as √2420, whereas (2420)^(1/2) in the exponential form. √2420 ≈ 49.1935, 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 2420 is broken down into its prime factors:

Step 1: Finding the prime factors of 2420 Breaking it down, we get 2 x 2 x 5 x 11 x 11: 2^2 x 5^1 x 11^2

Step 2: Now we found out the prime factors of 2420. The second step is to make pairs of those prime factors. Since 2420 is not a perfect square, therefore the digits of the number can’t be grouped in pair completely. Therefore, calculating 2420 using prime factorization directly for its square root 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 2420, we need to group it as 20 and 24.

Step 2: Now we need to find n whose square is closest to 24. We can say n is ‘4’ because 4 x 4 = 16, which is less than 24. Now the quotient is 4, after subtracting 24 - 16 the remainder is 8.

Step 3: Now let us bring down 20 which is the new dividend. Add the old divisor (4) with the same number 4 + 4 to get 8, which will be our new divisor.

Step 4: The new divisor will be 8n, we need to find the value of n.

Step 5: The next step is finding 8n × n ≤ 820. Let us consider n as 9, now 89 x 9 = 801.

Step 6: Subtract 820 from 801, the difference is 19, and the quotient is 49.

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 1900.

Step 8: Now we need to find the new divisor, which is 98 because 98 x 9 = 882.

Step 9: Subtracting 882 from 1900, we get the result 1018.

Step 10: Now the quotient is 49.1

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

So the square root of √2420 is approximately 49.19.

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 2420 using the approximation method.

Step 1: Now we have to find the closest perfect square of √2420. The smallest perfect square less than 2420 is 2401, and the largest perfect square more than 2420 is 2500. √2420 falls somewhere between 49 and 50.

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 (2420 - 2401) ÷ (2500 - 2401) = 19 ÷ 99 = 0.192

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 49 + 0.192 = 49.192, so the square root of 2420 is approximately 49.192.

• 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.

• Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that holds more prominence due to its uses in the real world. This is why it is known as the principal square root.

• Prime factorization: The expression of a number as the product of its prime numbers is called prime factorization.

• 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.