Square Root of 2.22

The square root is the inverse of the square of a number. 2.22 is not a perfect square. The square root of 2.22 is expressed in both radical and exponential form. In radical form, it is expressed as √2.22, whereas (2.22)^(1/2) is the exponential form. √2.22 ≈ 1.48997, 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 methods like long division and approximation 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. However, since 2.22 is not a perfect square and is a decimal, the prime factorization method is not applicable. Therefore, calculating 2.22 using prime factorization is not feasible.

The long division method is particularly used for non-perfect square numbers. In this method, we should find 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 pair the numbers from right to left. For 2.22, we consider 2.22 as the whole number.

Step 2: Now we need to find a number n whose square is less than or equal to 2. We can say n is '1' because 1 x 1 is less than or equal to 2. Now the quotient is 1, and the remainder is 2 - 1 = 1.

Step 3: Bring down the next pair, which is 22, to make the new dividend 122. Add the old divisor with the same number: 1 + 1 = 2. This will be the new divisor.

Step 4: The new divisor is 2n. We need to find the value of n.

Step 5: The next step is finding 2n × n ≤ 122. Let n be 4, so 24 × 4 = 96.

Step 6: Subtract 96 from 122, resulting in a difference of 26, and the quotient is 1.4.

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to bring down pairs of zeros. The new dividend is 2600.

Step 8: Now, find the new divisor which is 29 because 29 x 9 = 261.

Step 9: Subtracting 261 from 2600, we get the result 2339.

Step 10: Continue these steps until we achieve the desired precision.

The square root of 2.22 is approximately 1.4899.

The approximation method is another way to find the square roots. It is an easy method to find the square root of a given number. Let us learn how to find the square root of 2.22 using the approximation method.

Step 1: Identify the perfect squares closest to 2.22. The smallest perfect square is 1 (√1 = 1) and the largest perfect square is 4 (√4 = 2). √2.22 falls between 1 and 2.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (2.22 - 1) / (4 - 1) = 0.4067. Adding this to the lower bound 1, we get 1 + 0.4067 ≈ 1.4067. Thus, by approximation, the square root of 2.22 is approximately 1.4899.

• 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.
   
• Irrational number: An irrational number is a number that cannot be written in the form of p/q, q is not equal to zero, and p and q are integers.
   
• Decimal: A number that has a whole number and a fractional part separated by a decimal point, e.g., 2.22.
   
• Approximation: The method of finding an approximate value for a square root or other calculations, often used for non-perfect squares.
   
• Radical form: The expression of a square root using the radical symbol, e.g., √2.22.