Square Root of 96.16

The square root is the inverse of the square of the number. 96.16 is not a perfect square. The square root of 96.16 is expressed in both radical and exponential form.

In the radical form, it is expressed as √96.16, whereas (96.16)^(1/2) in the exponential form. √96.16 ≈ 9.804, 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 the long-division method and approximation method are used. Let us now learn the following methods:

1. Prime factorization method
2. Long division method
3. Approximation method

The product of prime factors is the prime factorization of a number. However, since 96.16 is not an integer, the prime factorization method is not suitable. We will need to use other methods such as long division and approximation for non-perfect square decimals like 96.16.

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: Begin by pairing the digits from right to left. For 96.16, consider the digits as 96 and 16.

Step 2: Find n whose square is less than or equal to 96. Here, n = 9 because 9 × 9 = 81, which is less than 96. The quotient is 9, and the remainder is 96 - 81 = 15.

Step 3: Bring down the decimal part 16, making it 1516. Double the quotient to get the new divisor: 2 × 9 = 18.

Step 4: Find a digit x such that 18x × x is less than or equal to 1516. Let's take x = 8, so 188 × 8 = 1504.

Step 5: Subtract 1504 from 1516, the remainder is 12, and the quotient is now 9.8.

Step 6: Continue the process and add decimals if needed until you reach the desired precision.

The square root of √96.16 is approximately 9.804.

The approximation method is an easy method to find the square root of a given number. Now let us learn how to find the square root of 96.16 using the approximation method.

Step 1: Find the closest perfect squares around 96.16. The closest lower perfect square is 81, and the closest higher perfect square is 100.

Step 2: √81 = 9 and √100 = 10. Therefore, √96.16 falls between 9 and 10.

Step 3: Use interpolation to approximate: (96.16 - 81) / (100 - 81) = 15.16 / 19 ≈ 0.797 Add this to the lower bound: 9 + 0.797 ≈ 9.797

The approximation gives us a value close to 9.804, the true square root.

• Square root: The inverse operation of squaring a number. Example: 4² = 16, and the inverse of the square is the square root, so √16 = 4.

• Irrational number: A number that cannot be written as a simple fraction; its decimal goes on forever without repeating. Example: √2, √3.

• Decimal: A number that has a whole number part and a fractional part. Example: 3.14, 5.67.

• Approximation: An estimated value close to the actual value. Example: π ≈ 3.14.

• Long division: A step-by-step method to find the square root of non-perfect squares.