Square Root of 9.6

The square root is the inverse operation of squaring a number. 9.6 is not a perfect square. The square root of 9.6 can be expressed in both radical and exponential forms. In radical form, it is expressed as √9.6, whereas in exponential form, it is (9.6)^(1/2). √9.6 ≈ 3.098, 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 generally used for perfect squares. However, for non-perfect square numbers like 9.6, methods such as the long division method and approximation method are used. Let's explore these methods: -

• Long division method 
• Approximation method

The long division method is used to find the square root of non-perfect squares. Here is how to find the square root of 9.6 using the long division method:

Step 1: Begin by setting up the number 9.6. Since it involves a decimal, consider 960 (by multiplying by 100 to eliminate the decimal temporarily).

Step 2: Find the largest number whose square is less than or equal to 9. In this case, it's 3 because 3^2 = 9.

Step 3: Subtract 9 from 9 to get 0 and bring down the next two digits (60).

Step 4: Double the divisor (3) to get 6, then determine the largest digit (n) such that 6n × n ≤ 60. The correct digit is 0 (since 60 is the nearest number divisible by 60), so the new divisor is 60.

Step 5: Subtract 60 from 60 to get 0, then bring down the next two digits (00) to continue the division.

Step 6: Continue this process, adding decimal places and zeroes as needed until the desired level of precision is reached.

The square root of 9.6 is approximately 3.098.

The approximation method is a simple way to find the square root of a non-perfect square. Here's how to find the square root of 9.6 using this method:

Step 1: Identify the perfect squares closest to 9.6. The smallest perfect square is 9, and the largest is 16. √9.6 lies between √9 (3) and √16 (4).

Step 2: Apply the interpolation formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). For 9.6, (9.6 - 9) / (16 - 9) = 0.6 / 7 ≈ 0.086.

Step 3: Add this decimal to the smaller whole number: 3 + 0.086 ≈ 3.086.

Thus, the approximate square root of 9.6 is 3.098.

• Square root: The square root is the inverse operation of squaring a number. For example, if 3² = 9, then √9 = 3.
   
• Irrational number: An irrational number cannot be expressed as a fraction p/q, where p and q are integers, and q is not zero.
   
• Approximation: Approximating involves finding a value close to the true value, often using methods like interpolation or rounding.
   
• Decimal: A decimal is a number that includes a fractional part separated by a decimal point, such as 3.098.
   
• Prime factorization: Prime factorization is the process of expressing a number as a product of its prime factors.