Square Root of 1004

The square root is the inverse of the square of the number. 1004 is not a perfect square. The square root of 1004 is expressed in both radical and exponential form. In the radical form, it is expressed as √1004, whereas (1004)^(1/2) in the exponential form. √1004 ≈ 31.70064, 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 and approximation methods are used. Let us now learn the following methods:

1. Prime factorization method
2. Long division method
3. Approximation method

The product of prime factors is the prime factorization of a number. Now let us look at how 1004 can be broken down into its prime factors:

Step 1: Finding the prime factors of 1004 Breaking it down, we get 2 x 2 x 251: 2² x 251

Step 2: Now we found out the prime factors of 1004. The second step is to make pairs of these prime factors. Since 1004 is not a perfect square, the digits of the number can’t be grouped in pairs.

Therefore, calculating 1004 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. In the case of 1004, we need to group it as 04 and 10.

Step 2: Now we need to find n whose square is less than or equal to 10. We can say n as ‘3’ because 3 x 3 = 9 is less than 10. Now the quotient is 3, and the remainder is 10 - 9 = 1.

Step 3: Now let us bring down 04 which is the new dividend. Add the old divisor with the same number: 3 + 3 = 6, which will be our new divisor.

Step 4: The new divisor will be the sum of the previous divisor and quotient. Now we get 6n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 104. Let us consider n as 1, now 6 x 1 x 1 = 6.

Step 6: Subtract 104 from 66, the difference is 38, and the quotient is 31.

Step 7: Since the new 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 3800.

Step 8: Now we need to find the new divisor, which can be 631. 631 x 6 = 3786.

Step 9: Subtracting 3786 from 3800, we get the result 14.

Step 10: Now the quotient is 31.6. 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 √1004 is approximately 31.70.

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 1004 using the approximation method.

Step 1: Now we have to find the closest perfect square of √1004. The smallest perfect square less than 1004 is 961, and the largest perfect square greater than 1004 is 1024. So, √1004 falls somewhere between 31 and 32.

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

Using the formula (1004 - 961) ÷ (1024 - 961) = 43 ÷ 63 ≈ 0.6825 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 31 + 0.6825 ≈ 31.68. So the approximate square root of 1004 is 31.68.

• 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 factorization: Breaking down a number into its basic building blocks or prime numbers. For example, the prime factorization of 1004 is 2 x 2 x 251.

• Decimal: A number that has a whole number and a fractional part separated by a decimal point. For example: 31.70, 3.14, and 0.001 are decimals.