Square Root of 7/2

The square root is the inverse of the square of a number. 7/2 is not a perfect square. The square root of 7/2 is expressed in both radical and exponential form. In the radical form, it is expressed as √(7/2), whereas in exponential form, it is expressed as (7/2)^(1/2). √(7/2) = 1.8708, 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.

We can find the square root of a fraction by finding the square roots of the numerator and the denominator separately. For non-perfect square numbers, approximation methods can be used. Let us now learn the following methods:

1. Simplification method

2. Approximation method

The simplification method involves finding the square roots of the numerator and the denominator separately.

Step 1: Find the square root of the numerator 7. Since 7 is not a perfect square, we approximate √7 ≈ 2.64575.

Step 2: Find the square root of the denominator 2. √2 ≈ 1.41421.

Step 3: Combine the results: √(7/2) = √7 / √2 ≈ 2.64575 / 1.41421 ≈ 1.8708.

The approximation method is straightforward and involves estimating the square root numerically.

Step 1: Estimate √7 ≈ 2.64575 and √2 ≈ 1.41421.

Step 2: Divide the estimates: 2.64575 / 1.41421 ≈ 1.8708.

Step 3: Therefore, the square root of 7/2 is approximately 1.8708.

• Square root: A square root is the value that, when multiplied by itself, gives the original number. Example: √4 = 2.

• Irrational number: A number that cannot be expressed as a simple fraction. Its decimal form is non-repeating and non-terminating, like √2.

• Fraction: A part of a whole expressed as a ratio of two integers, such as 7/2.

• Approximation: A value or number that is close to the exact amount, often used when an exact value is not needed or is difficult to obtain.

• Division: A mathematical operation where a number is divided into equal parts, often used in finding average values or simplifying expressions.