Square Root of 4.5

The square root is the inverse of the square of the number. 4.5 is not a perfect square. The square root of 4.5 is expressed in both radical and exponential form. In the radical form, it is expressed as √4.5, whereas (4.5)^(1/2) in the exponential form. √4.5 = 2.12132, 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, the prime factorization method is not used for non-perfect square numbers, where long division method and approximation method are used. Let us now learn the following methods:

• Prime factorization method
•  Long division method
• Approximation method

The long division method is particularly used for non-perfect square numbers. In this method, we should check 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. Since 4.5 is a single-digit number with a decimal, we can start directly.

Step 2: Find a number whose square is less than or equal to 4. The closest number is 2 since 2 × 2 = 4. The quotient is 2, and the remainder is 0.

Step 3: Bring down the next pair (50) to make it 050. Add the old divisor (2) with itself to get 4, which will be our new divisor.

Step 4: Find 4n such that 4n × n is less than or equal to 50. Let n be 1, so 41 × 1 = 41.

Step 5: Subtract 41 from 50 to get a remainder of 9.

Step 6: Since the dividend is less than the divisor, add a decimal point and bring down two zeros, making the new dividend 900.

Step 7: The new divisor is 42, so find 42n × n ≤ 900. Let n be 2. Then 422 × 2 = 844.

Step 8: Subtract 844 from 900 to get a remainder of 56.

Step 9: Continue the process until the desired decimal places are achieved. The quotient so far is 2.12.

The square root of 4.5 is approximately 2.12132.

The approximation method is another method for finding the square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 4.5 using the approximation method.

Step 1: Find the closest perfect squares around 4.5.

The closest perfect squares are 4 and 9. Therefore, √4.5 falls between √4 (which is 2) and √9 (which is 3).

Step 2: Use interpolation to estimate the square root of 4.5.

Using the formula: (4.5 - 4) / (9 - 4) = 0.1 Approximate square root: 2 + 0.1 * (3 - 2) = 2.1

Therefore, the approximate square root of 4.5 is 2.12132.

• Square root: A square root is the inverse of a square. For example, 4^2 = 16, and the inverse of the square is the square root, so √16 = 4.

• Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers.

• Principal square root: A number has both positive and negative square roots; however, the positive square root is more commonly used due to its applications in the real world. This is known as the principal square root.

• Rational number: A rational number can be expressed as the ratio of two integers, with a non-zero denominator. Examples include 1/2, 3/4, and 5.

• Decimal: If a number has a whole number and a fractional part in a single expression, it is called a decimal. Examples include 7.86, 8.65, and 9.42.