Square Root of 1.4

The square root is the inverse of the square of the number. 1.4 is not a perfect square. The square root of 1.4 is expressed in both radical and exponential form. In the radical form, it is expressed as √1.4, whereas (1.4)^(1/2) in the exponential form. √1.4 ≈ 1.1832, 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 typically used for perfect square numbers. However, for non-perfect square numbers like 1.4, the long-division method and approximation method are used. Let us now learn the following methods:

• Long division method
   
• Approximation method

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 numbers from right to left. In the case of 1.4, we work with it as is because it already has two decimal places.

Step 2: Determine the largest integer whose square is less than or equal to 1.4. In this case, consider 1 because 1 × 1 = 1, which is less than 1.4.

Step 3: Subtract 1 from 1.4, which leaves a remainder of 0.4, and bring down another pair of zeros, making it 40.

Step 4: Double the current quotient (1) to get 2, which becomes the beginning of our new divisor.

Step 5: Find a digit (x) such that 2x × x is less than or equal to 40. The digit 1 works because 21 × 1 = 21.

Step 6: Subtract 21 from 40, leaving a remainder of 19. Step 7: Bring down another pair of zeros to make it 1900.

Step 8: Repeat these steps to reach the desired level of precision.

The result will be approximately 1.1832.

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 1.4 using the approximation method.

Step 1: Identify the perfect squares closest to 1.4. The closest perfect square less than 1.4 is 1, and the closest perfect square greater than 1.4 is 4. Therefore, √1.4 falls between 1 and 2.

Step 2: Estimate the value. Since 1.4 is closer to 1 than to 4, the square root will be slightly greater than 1.

Using methods such as linear interpolation, we find that √1.4 is approximately 1.1832.

• Square root: A square root is the inverse of a square. For 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. For example, √1.4 is irrational.

• Rational number: A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, where q is not zero.

• Approximation: Approximation refers to the process of finding a value that is close enough to the correct answer, usually within a certain tolerance.

• Long division method: The long division method is a technique used to find the square root of a number by dividing it into parts, allowing for the calculation of square roots of non-perfect squares.