Square Root of 84.64

The square root is the inverse of squaring a number. 84.64 is not a perfect square. The square root of 84.64 can be expressed in both radical and exponential forms.

In radical form, it is expressed as √84.64, whereas in exponential form it is expressed as (84.64)^(1/2). √84.64 = 9.2, 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 typically used for perfect square numbers. However, for non-perfect square numbers, methods such as 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 long division method is particularly used for non-perfect square numbers. In this method, we find 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: To begin with, we need to group the numbers from right to left, taking two digits at a time. For 84.64, we consider 84 and 64.

Step 2: Find a number whose square is closest to or less than 84. It's 9, because 9 × 9 = 81, which is less than 84. The quotient is 9, and the remainder is 84 - 81 = 3.

Step 3: Bring down the next pair, 64, to make it 364.

Step 4: Double the quotient (which is 9) to get 18, and consider 18_ as the new divisor.

Step 5: Find a digit to place in the blank so that (18_ × _) is less than or equal to 364. The digit is 2 because 182 × 2 = 364.

Step 6: Subtract 364 from 364 to get 0. Since the remainder is 0, the square root of 84.64 is 9.2.

The approximation method is a simpler method for finding square roots. Let us learn how to find the square root of 84.64 using the approximation method.

Step 1: Identify perfect squares around 84.64. The closest perfect squares are 81 (which is 9²) and 100 (which is 10²). √84.64 is between 9 and 10.

Step 2: Using a more precise approximation, we find that 9.2 is very close to √84.64 since 9.2 × 9.2 = 84.64.

• Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √16 = 4.

• Rational number: A rational number can be expressed as a fraction where the numerator and the denominator are integers, and the denominator is not zero.

• Perfect square: A perfect square is a number that has an integer as its square root. Example: 81 is a perfect square because √81 = 9.

• Long division method: A step-by-step method used to find the square root of a number, especially when dealing with non-perfect squares.

• Approximation method: A technique used to estimate the square root of a number by comparing it to nearby perfect squares.