Square Root of 1.44

The square root is the inverse of the square of the number. 1.44 is a perfect square. The square root of 1.44 is expressed in both radical and exponential form. In the radical form, it is expressed as √1.44, whereas (1.44)^(1/2) in the exponential form. √1.44 = 1.2, 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 is used for perfect square numbers. For non-perfect square numbers, the 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 1.44 is broken down into its prime factors.

Step 1: Finding the prime factors of 1.44 Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 3: 2^4 x 3^2

Step 2: Now we found out the prime factors of 1.44. The second step is to make pairs of those prime factors. Since 1.44 is a perfect square, we can group all factors into pairs: (2 x 2) and (3 x 3).

Step 3: The square root of 1.44 is the product of one number from each pair: 2 x 3 = 6.

Step 4: Since we need to account for the decimal position, the final square root of 1.44 is 1.2.

The long division method is particularly used for non-perfect square numbers but can be used for perfect squares as well. In this method, we find the square root step by step.

Step 1: To begin with, we need to pair the numbers from right to left. In the case of 1.44, we need to consider it as 1.44.

Step 2: Now, find the largest integer whose square is equal to or less than 1. In this case, it is 1 because 1 x 1 = 1.

Step 3: Subtract 1 from 1 to get 0. Bring down the next pair of digits to make it 44.

Step 4: Double the quotient to get 2. We need to find a digit n such that 2n multiplied by n gives a result less than or equal to 44.

Step 5: The closest value is 2, as 22 x 2 = 44.

Step 6: Subtract 44 from 44 to get 0. The quotient so far is 1.2.

Step 7: The square root of 1.44 is 1.2.

The approximation method is another method for finding 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 1.44 using the approximation method.

Step 1: Identify the closest perfect squares of √1.44. The closest smaller perfect square is 1 (1^2) and the closest larger perfect square is 1.69 (1.3^2).

Step 2: Since 1.44 is exactly between 1 and 1.69, we can say the square root of 1.44 is exactly 1.2.

• Square root: A square root is the inverse of a square. Example: 1.2^2 = 1.44, and the inverse of the square is the square root, that is, √1.44 = 1.2.
   
• Rational number: A rational number is a number that can be written 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. For example, 4 is a perfect square because it is 2^2.
   
• Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 1.2, 3.4, and 5.6 are decimals.
   
• Factor: A factor of a number is a number that divides the original number exactly, without leaving a remainder. For example, factors of 6 are 1, 2, 3, and 6.