Square Root of 4481

The square root is the inverse of the square of the number. 4481 is not a perfect square. The square root of 4481 is expressed in both radical and exponential form. In radical form, it is expressed as √4481, whereas in exponential form, it is (4481)^(1/2). √4481 ≈ 66.96984, 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 such as the long-division method and approximation method are used. Let us now learn these 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 4481 is broken down into its prime factors.

Step 1: Finding the prime factors of 4481 Breaking it down, we find that 4481 cannot be easily expressed as a product of repeated prime factors, making it unsuitable for the prime factorization method to find the square root accurately. Since 4481 is not a perfect square, calculating it using prime factorization is impractical for finding the square root.

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 digits of 4481 from right to left, which is already a single group.

Step 2: Find a number whose square is less than or equal to 44. The number is 6, as 6 × 6 = 36.

Step 3: Subtract 36 from 44, bringing down the next group to get 881.

Step 4: Double the current quotient (6), and use it as the first part of the new divisor, i.e., 12_.

Step 5: Find a digit n such that (12n) × n ≤ 881. Here n is 7, as 127 × 7 = 889, which is greater than 881. So try n = 6, then 126 × 6 = 756.

Step 6: Subtract 756 from 881 to get a remainder of 125. The current quotient is 66.

Step 7: Since the remainder is not zero, add a decimal point to the quotient and bring down two zeros to make it 12500.

Step 8: Find a new divisor, 132_, and repeat the process with the new remainder.

Step 9: Continue until you have the desired precision. The quotient becomes approximately 66.96984.

So, the square root of √4481 ≈ 66.96984.

The approximation method is another method for finding 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 4481 using the approximation method.

Step 1: Find the closest perfect squares around 4481. The smallest perfect square less than 4481 is 4356 (66²), and the largest perfect square greater than 4481 is 4624 (68²). √4481 falls between 66 and 68.

Step 2: Apply the formula for approximation: (Given number - smaller perfect square) / (difference between perfect squares). (4481 - 4356) / (4624 - 4356) = 125 / 268 ≈ 0.4664

Step 3: Add this decimal to the smaller perfect square root: 66 + 0.4664 ≈ 66.4664 The square root of 4481 is approximately 66.97.

• Square root: A square root is the inverse of a square. Example: 4² = 16 and the inverse of the square is the square root, which 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.

• Long division method: A method used to find the square roots of non-perfect squares involving systematic division steps.

• Approximation: A method to estimate the square root of a number by comparing it to known perfect squares.

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