Square Root of 4.4

The square root is the inverse of the square of the number. 4.4 is not a perfect square. The square root of 4.4 is expressed in both radical and exponential form. In the radical form, it is expressed as √4.4, whereas (4.4)¹/² in the exponential form. √4.4 ≈ 2.0976, 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. Since 4.4 is a decimal and not a perfect square, it cannot be broken down into integer prime factors. Therefore, calculating 4.4 using prime factorization is impractical.

The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.

Step 1: Start by grouping the numbers from right to left. For 4.4, we consider it as 44 with two decimal places.

Step 2: Find n whose square is less than or equal to 4. We find n as 2 because 2 × 2 = 4. Subtract 4 from 4 to get a remainder of 0.

Step 3: Bring down the 40 (due to decimal point) making the new dividend 40. Add the old divisor with the number 2, resulting in a new divisor of 4.

Step 4: Find 4n × n ≤ 40. The value of n is 0 as 4 × 0 × 0 = 0.

Step 5: Subtract 0 from 40. The difference is 40, and the quotient is 2.0.

Step 6: Add a decimal point to the quotient. Bring down two zeros, making the dividend 4000.

Step 7: The new divisor becomes 40 (4 with the repeated quotient digit 0 added). The closest n satisfying 40n × n ≤ 4000 is 9, as 409 × 9 = 3681.

Step 8: Subtract 3681 from 4000 to get a remainder of 319.

Step 9: The quotient is approximately 2.09.

Continue the process for more precision.

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 4.4 using the approximation method.

Step 1: Find the closest perfect squares around 4.4. The smallest perfect square is 4 (√4 = 2), and the largest is 9 (√9 = 3). √4.4 falls between 2 and 3.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (4.4 - 4) / (9 - 4) = 0.08. Adding this value to the smaller square root: 2 + 0.08 = 2.08, so the approximate square root of 4.4 is 2.08.

• 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.

• 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.

• Long division method: A technique used to find the square root of non-perfect square numbers by dividing the number into groups of two digits from right to left.

• Approximation method: A method used to estimate the value of the square root by identifying nearby perfect squares and using them to refine the estimate.