Square Root of 4489

The square root is the inverse of the square of a number. 4489 is a perfect square. The square root of 4489 can be expressed in both radical and exponential form. In radical form, it is expressed as √4489, whereas in exponential form, it is (4489)^(1/2). √4489 = 67, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

The prime factorization method can be used for perfect square numbers. However, for non-perfect square numbers, the long-division method and approximation method are also 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 4489 is broken down into its prime factors.

Step 1: Finding the prime factors of 4489

Breaking it down, we get 67 × 67: 67^2

Step 2: Now we found out the prime factors of 4489. The next step is to make pairs of those prime factors. Since 4489 is a perfect square, we can pair the digits. Therefore, calculating 4489 using prime factorization gives us √4489 = 67.

The long division method is particularly used for non-perfect square numbers, but it can also verify perfect squares. In this method, we will 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 4489, we need to group it as 44 and 89.

Step 2: Now we need to find n whose square is less than or equal to 44. We can say n is ‘6’ because 6 × 6 = 36, which is less than 44. Now the quotient is 6, and the remainder after subtracting 36 from 44 is 8.

Step 3: Now let us bring down 89 to make the new dividend 889. Add the old divisor with the same number 6 + 6 to get 12, which will be our new divisor.

Step 4: The new divisor will be 12n. We need to find the value of n such that 12n × n is less than or equal to 889. Let us consider n as 7, now 12 × 7 × 7 = 889.

Step 5: Subtract 889 from 889, the difference is 0, and the quotient is 67. Therefore, the square root of √4489 is 67.

The approximation method is another method for finding square roots, used especially for non-perfect squares, but it is straightforward for perfect squares. Since 4489 is a perfect square, the approximation method provides quick verification.

Step 1: Identify the closest perfect square of √4489. Since 4489 is already a perfect square, we know √4489 = 67.

Step 2: Therefore, the square root of 4489 is 67.

• 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.

• Rational number: A rational number is a number that can be expressed in the form of p/q, where q is not equal to zero and p and q are integers.

• Perfect square: A perfect square is a number that is the square of an integer. Example: 36 is a perfect square because it is 6^2.

• Prime factorization: Prime factorization is the process of expressing a number as the product of its prime factors.

• Long division method: A method used to find the square root of a number that involves dividing and averaging.