Square Root of 30.25

The square root is the inverse of the square of the number. 30.25 is a perfect square. The square root of 30.25 is expressed in both radical and exponential form. In the radical form, it is expressed as √30.25, whereas (30.25)^(1/2) in the exponential form. √30.25 = 5.5, 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, long division method, and approximation method can be used to find square roots. However, since 30.25 is a perfect square, we can simply check its square root directly. 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 30.25 can be expressed:

Step 1: Recognizing that 30.25 = (5.5)^2

Step 2: Since 30.25 is a perfect square, the square root is directly obtained as 5.5.

Thus, using prime factorization is unnecessary here as it does not yield additional insight.

The long division method is useful for non-perfect square numbers, but can also confirm perfect squares. Here, let's see how it works for 30.25:

Step 1: To begin with, group the numbers from right to left. For 30.25, we consider 30 and 25 separately for ease.

Step 2: Find n whose square is close to 30. Here, 5 × 5 = 25, which is close to 30. Now the quotient is 5.

Step 3: The remainder is 30 - 25 = 5. Bring down the next pair of digits (25) to make it 525.

Step 4: Double the divisor 5 to get 10. Now, find a digit n such that 10n × n is less than 525. The best choice is n = 5, since 105 × 5 = 525.

Step 5: Subtract to get the remainder of 0, confirming the quotient as 5.5.

The approximation method is used for finding the square roots of non-perfect squares, but here we confirm 30.25 is perfect.

Step 1: Find the closest perfect squares around 30.25.

We know 25 = 5^2 and 36 = 6^2.

Thus, √30.25 is between 5 and 6.

Step 2: By direct calculation or estimation, √30.25 is found to be precisely 5.5, confirming it as a perfect square.

• Square root: A square root is the inverse of a square. Example: 5.5^2 = 30.25 and the inverse of the square is the square root that is √30.25 = 5.5.
   
• 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, 25 is a perfect square as 5^2 = 25.
   
• Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 5.5 are decimals.
   
• Long division method: A method used to find the square roots of numbers, particularly useful for non-perfect squares, though it can confirm perfect squares as well.