Square Root of 930.25

The square root is the inverse of the square of a number. 930.25 is a perfect square. The square root of 930.25 is expressed in both radical and exponential form. In the radical form, it is expressed as √930.25, whereas (930.25)^(1/2) in the exponential form. √930.25 = 30.5, 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.

For perfect square numbers, the prime factorization method can be useful, but since 930.25 is a perfect square with decimals, the best methods to consider are the long-division method and direct calculation. Let us now learn the following methods:

• Long division method
• Direct calculation method

The long division method is useful for finding the square roots of non-perfect square numbers, but it can also be used for confirming perfect squares. Let us learn how to find the square root using the long division method for 930.25:

Step 1: We need to pair the digits of 930.25 starting from the decimal point. So, we have pairs (9, 30) and (.25).

Step 2: Find a number whose square is equal to or less than the first pair 9. We know that 3 x 3 = 9. Subtract 9 from 9 to get 0, and bring down the next pair, which is 30.

Step 3: Double the quotient (3) to get 6. Now, determine a digit X such that 6X multiplied by X is less than or equal to 30. The value of X is 5, since 65 * 5 = 325.

Step 4: Subtract 325 from 930 to get 5. Bring down the next pair (.25) to make it 525.

Step 5: Double the current quotient (35) to get 70. Find a digit X such that 70X multiplied by X is less than or equal to 525. The value of X is 7, since 707 * 7 = 4949.

Step 6: Subtract 4949 from 525 to get 0.

Step 7: The quotient is 30.5, which is the square root of 930.25.

Since 930.25 is a perfect square, its square root can also be found directly by recognizing the pattern of multiplication:

Step 1: Break down 930.25 as (30 * 30) + (0.5 * 0.5).

Step 2: Recognize that 30.5 * 30.5 = 930.25. Therefore, the square root of 930.25 is 30.5.

Students often make mistakes while finding the square root of numbers. Here are some key points to remember to avoid errors:

• Square root: A square root is the inverse operation of squaring a number. For example, 30.5² = 930.25, and the square root of 930.25 is 30.5.
   
• Rational number: A rational number is a number that can be written as a fraction where both the numerator and the denominator are integers, and the denominator is not zero.
   
• Perfect square: A perfect square is a number that is the square of an integer. For example, 930.25 is a perfect square because it is 30.5².
   
• Principal square root: This is the non-negative square root of a number. For example, the principal square root of 930.25 is 30.5.
   
• Decimal: A decimal number is a number that contains a decimal point, representing a fraction of a base-ten number. For example, 930.25 is a decimal number.