Square Root of 1044

The square root is the inverse of the square of a number. 1044 is not a perfect square. The square root of 1044 is expressed in both radical and exponential form. In radical form, it is expressed as √1044, whereas (1044)^(1/2) in exponential form. √1044 ≈ 32.31099, 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, for non-perfect square numbers, methods like 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 1044 is broken down into its prime factors.

Step 1: Finding the prime factors of 1044 Breaking it down, we get 2 x 2 x 3 x 3 x 29: 2^2 x 3^2 x 29^1

Step 2: Now we have the prime factors of 1044. The second step is to make pairs of those prime factors. Since 1044 is not a perfect square, the digits of the number can’t be grouped into pairs.

Therefore, calculating 1044 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 1044, we need to group it as 44 and 10.

Step 2: Now we need to find n whose square is ≤ 10. We can say n is 3 because 3 x 3 = 9, which is less than or equal to 10. Now the quotient is 3; after subtracting 9 from 10, the remainder is 1.

Step 3: Now let us bring down 44, which is the new dividend. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend 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 ≤ 144. Let us consider n as 2; now 6 x 2 x 2 = 24.

Step 6: Subtract 24 from 144; the difference is 120, and the quotient is 32.

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 12000.

Step 8: Now we need to find the new divisor. Let us find n such that 649n x n ≤ 12000. Let n be 1, so 649 x 1 = 649.

Step 9: Subtracting 649 from 12000, we get the result 11351.

Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values; continue until the remainder is zero.

So the square root of √1044 is approximately 32.31.

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 1044 using the approximation method.

Step 1: Now we have to find the closest perfect squares around √1044. The smallest perfect square less than 1044 is 1024, and the largest perfect square greater than 1044 is 1089. √1044 falls somewhere between 32 and 33.

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (1044 - 1024) / (1089 - 1024) = 20 / 65 ≈ 0.3077. Adding the result to the smaller integer, 32 + 0.3077 = 32.3077.

Therefore, the square root of 1044 is approximately 32.31.

• Square root: A square root is the inverse of a square. For example: 6^2 = 36, and the inverse of the square is the square root, that is √36 = 6.
   
• 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 expression of a number as the product of its prime numbers. For example, the prime factorization of 1044 is 2 × 2 × 3 × 3 × 29.
   
• 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.