Square Root of 12.25

The square root is the inverse of the square of the number. 12.25 is a perfect square. The square root of 12.25 is expressed in both radical and exponential form. In radical form, it is expressed as √12.25, whereas (12.25)^(1/2) in exponential form. √12.25 = 3.5, 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, methods like 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 12.25 is broken down into its prime factors.

Step 1: Recognize 12.25 as 1225/100.

Step 2: Find the prime factors of 1225 and 100. 1225 = 5 x 5 x 7 x 7, and 100 = 2 x 2 x 5 x 5.

Step 3: Taking the square root, √12.25 = √(1225/100) = (5 x 7) / (2 x 5) = 7/2 = 3.5.

The long division method is particularly useful for non-perfect square numbers, but it can also be used to understand perfect squares. Let us now learn how to find the square root using the long division method, step by step.

Step 1: Group the numbers from right to left. For 12.25, consider 1225.

Step 2: Find n whose square is closest to 12. We can say n is 3 because 3 x 3 = 9, which is less than 12.

Step 3: Bring down the next pair (25) to make it 325. Double the current quotient (3), making it 6, and use it to find the next digit.

Step 4: Estimate the next digit (5) such that 65 x 5 = 325.

Step 5: The quotient is 3.5, which is the square root of 12.25.

The approximation method is another method for finding square roots and is an easy method to find the square root of a given number. Now let us learn how to find the square root of 12.25 using the approximation method.

Step 1: Find two perfect squares between which 12.25 lies. It is between 9 and 16.

Step 2: Since 12.25 is closer to 16, approximate starting from √16 = 4. Decrease gradually to find the precise value.

Step 3: Using the approximation, √12.25 is exactly 3.5.

• Square root: A square root is the inverse of a square. Example: 3.5² = 12.25, and the inverse of the square is the square root, that is √12.25 = 3.5.
   
• Rational number: A rational number is a number that can be written in the form of p/q, q is not equal to zero, and p and q are integers.
   
• Perfect square: A number that is the square of an integer or a rational number. Example: 12.25 is a perfect square because it is 3.5².
   
• Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 3.5, 7.86, and 9.42 are decimals.
   
• Quotient: The result obtained by dividing one quantity by another. For example, in 12.25 ÷ 3.5 = 3.5, the quotient is 3.5.