Square Root of 2482

The square root is the inverse of the square of a number. 2482 is not a perfect square. The square root of 2482 is expressed in both radical and exponential form. In the radical form, it is expressed as √2482, whereas in the exponential form, it is expressed as (2482)^(1/2). √2482 ≈ 49.823, 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 2482 is broken down into its prime factors.

Step 1: Finding the prime factors of 2482 Breaking it down, we get 2 x 1241. Since 1241 is a prime number, the prime factorization of 2482 is 2 x 1241.

Step 2: For non-perfect squares like 2482, prime factorization does not allow us to find the square root directly.

Therefore, calculating √2482 using prime factorization is not feasible.

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. For 2482, we need to group it as 24 and 82.

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

Step 3: Now, let us bring down 82, which becomes the new dividend. Add the old divisor with the same number (4 + 4) to get 8, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient, which is 8n. We need to find the value of n.

Step 5: The next step is finding 8n x n ≤ 882. Let us consider n as 1, now 8 x 1 x 1 = 81.

Step 6: Subtract 81 from 82; the difference is 1, and the quotient is 41.

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 100.

Step 8: Now, we need to find the new divisor, which is 829 because 829 x 1 = 829.

Step 9: Subtracting 829 from 1000, we get the result 171.

Step 10: Now the quotient is 49.8.

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 √2482 is approximately 49.82.

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 2482 using the approximation method.

Step 1: Now we have to find the closest perfect squares to √2482. The smallest perfect square less than 2482 is 2401, and the largest perfect square more than 2482 is 2500. √2482 falls somewhere between 49 and 50.

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).

Going by the formula (2482 - 2401) / (2500 - 2401) = 81/99 ≈ 0.818.

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 + 0.818 = 49.818, so the square root of 2482 is approximately 49.82.

• Square root: A square root is the inverse of a square. 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 always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.

• Prime number: A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.

• 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.