Square Root of 20.16

The square root is the inverse of the square of a number. 20.16 is not a perfect square. The square root of 20.16 is expressed in both radical and exponential form. In radical form, it is expressed as √20.16, whereas (20.16)^(1/2) is the exponential form. √20.16 ≈ 4.49, 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 used for perfect square numbers. However, for non-perfect square numbers like 20.16, the long division method and approximation method are used. Let us now learn the following methods:

• Long division method
• Approximation method

The long division method is particularly used for non-perfect square numbers. This method involves checking 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: Group the numbers from right to left. In the case of 20.16, consider 20 and 16 separately.

Step 2: Find the largest number whose square is less than or equal to 20. This number is 4 because 4 x 4 = 16, which is less than 20.

Step 3: Subtract 16 from 20, giving a remainder of 4. Bring down the next pair of digits (which is 16) to get a new dividend of 416.

Step 4: Double the current quotient (4) to get 8, which will be the start of our new divisor.

Step 5: Find a digit to append to 8 to form a new divisor that, when multiplied by the same digit, results in a product less than or equal to 416. The suitable digit is 5, giving 85 x 5 = 425, which is close to 416.

Step 6: Subtract 425 from 416 to get a remainder. Continue the process until the desired decimal precision is reached.

So the approximate square root of √20.16 is 4.49.

The approximation method is another way to find square roots. It is an easy method to estimate the square root of a given number. Let us learn how to find the square root of 20.16 using the approximation method.

Step 1: Find the closest perfect squares to √20.16.

The smallest perfect square less than 20.16 is 16, and the largest is 25.

√20.16 falls somewhere between 4 and 5.

Step 2: Apply the formula:

(Given number - smallest perfect square) / (Largest perfect square - smallest perfect square).

Using this formula: (20.16 - 16) / (25 - 16) = 4.16 / 9 ≈ 0.46

Adding this decimal to the smallest square root gives us 4 + 0.46 = 4.46.

Therefore, the approximate square root of 20.16 is 4.46.

• Square root: The square root is the inverse operation of squaring a number. For example, if 4² = 16, then the square root of 16 is √16 = 4.
   
• Irrational number: An irrational number cannot be expressed as a simple fraction, where both the numerator and the denominator are integers. For example, √20.16 is irrational.
   
• Decimal approximation: A decimal approximation is an estimate of a number in decimal form, which is used when the exact value is difficult to represent, such as √20.16 ≈ 4.49.
   
• Long division method: A mathematical method used to divide large numbers and find square roots, especially for non-perfect squares like 20.16.
   
• Approximation method: A technique used to estimate the square root of numbers that are not perfect squares, often involving finding nearby perfect squares.