Square Root of 9/2

The square root is the inverse of the square of the number. 9/2 is not a perfect square. The square root of 9/2 is expressed in both radical and exponential form. In radical form, it is expressed as √(9/2), whereas (9/2)^(1/2) in exponential form. √(9/2) = √(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 typically used for non-perfect square numbers where long-division and approximation methods 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. In this method, we find the square root step by step. Let us see how to find the square root of 9/2 using the long division method:

Step 1: Convert the fraction to a decimal, which is 4.5.

Step 2: Find a number whose square is closest to 4.5.

Step 3: The square root of 4 is 2, which is the closest lower perfect square.

Step 4: Use the long division process to refine the result and find the decimal points.

The square root of 4.5 is approximately 2.12132.

The approximation method is another way to find square roots. It is an easier method to find the square root of a given number. Now let us learn how to find the square root of 9/2 using the approximation method.

Step 1: Convert 9/2 to a decimal, which is 4.5.

Step 2: Find the closest perfect squares around 4.5. The smallest perfect square less than 4.5 is 4, and the largest perfect square greater than 4.5 is 9. Therefore, √4.5 falls between 2 and 3.

Step 3: Use the approximation formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). (4.5 - 4) / (9 - 4) = 0.1

Step 4: Add this to the lower bound (2 + 0.1 = 2.1).

Thus, the square root of 4.5 is approximately 2.12132.

• Square root: The square root is the inverse operation of squaring a number. For example, if 4 is squared to get 16, then the square root of 16 is 4.

• Irrational number: An irrational number is a number that cannot be expressed as a simple fraction of two integers. For example, √2 is irrational.

• Principal square root: The principal square root of a non-negative number is the non-negative root. For example, the principal square root of 9 is 3.

• Fraction: A fraction represents a part of a whole and consists of a numerator and a denominator. For example, 1/2.

• Decimal: A decimal number is a representation of a fraction using powers of ten. For example, 0.5 is the decimal representation of 1/2.