Square Root of 1083

The square root is the inverse of the square of the number. 1083 is not a perfect square. The square root of 1083 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1083, whereas (1083)^(1/2) in the exponential form. √1083 ≈ 32.89377, 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 1083 is broken down into its prime factors:

Step 1: Finding the prime factors of 1083 Breaking it down, we get 3 x 3 x 3 x 3 x 13 = 3^4 x 13

Step 2: Now we found out the prime factors of 1083. The next step is to make pairs of those prime factors. Since 1083 is not a perfect square, the digits of the number can’t be grouped in pairs completely.

Therefore, calculating 1083 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 1083, we need to group it as 83 and 10.

Step 2: Now we need to find n whose square is ≤ 10. We can say n as ‘3’ because 3 × 3 = 9 is lesser than 10. Now the quotient is 3, and after subtracting 9 from 10, the remainder is 1.

Step 3: Now let us bring down 83, making the new dividend 183. Add the previous divisor (3) with the same number to get 6, which will be our new divisor.

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

Step 5: The next step is finding 6n × n ≤ 183. Let us consider n as 3; now, 63 × 3 = 189, which is too large. Trying n as 2, we get 62 × 2 = 124.

Step 6: Subtract 124 from 183; the difference is 59, 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 5900.

Step 8: Find the new divisor, which is 649, because 649 × 9 = 5841. Step 9: Subtracting 5841 from 5900, we get the result 59.

Step 10: Now the quotient is 32.9.

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 √1083 is approximately 32.89.

The approximation method is another method for finding the square roots, and 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 1083 using the approximation method.

Step 1: Now we have to find the closest perfect square of √1083. The smallest perfect square less than 1083 is 1024, and the largest perfect square greater than 1083 is 1089. √1083 falls somewhere between 32 and 33.

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, (1083 - 1024) ÷ (1089 - 1024) = 59 / 65 = 0.9077. 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 32 + 0.91 = 32.91.

So the square root of 1083 is approximately 32.91.

• Square root: A square root is the inverse of a square. For 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 is more prominent due to its use 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 factors. For example, 1083 = 3 × 3 × 3 × 3 × 13.
   
• Long division method: A step-by-step method used to find the square root of a non-perfect square by grouping and dividing the number methodically.