How is it irrational number

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ScanSolve AI Tutor · Accepted Answer

Step 1: To determine if a number is rational or irrational, we check if it can be expressed as a simple fraction of two integers. Step 2: A rational number can be written as p/q, where p and q are integers and q ≠ 0. For example, 0.5 is rational because it can be written as 1/2. Step 3: An irrational number cannot be expressed as a simple fraction of two integers. Its decimal representation is non-terminating and non-repeating. For example, π (pi) is irrational. Step 4: The number in question is √(23). We need to see if 23 is a perfect square. A perfect square is a number that can be obtained by squaring an integer (e.g., 4 is a perfect square because 2² = 4). Step 5: The integers closest to √(23) are 4 (since 4² = 16) and 5 (since 5² = 25). Since 23 falls between 16 and 25, and is not equal to either, it is not a perfect square. Step 6: Because 23 is not a perfect square, its square root, √(23), will result in a decimal that goes on forever without repeating. This means it cannot be written as a simple fraction of two integers. √(23) is an irrational number because it cannot be expressed as a fraction of two integers.

How is it irrational number

Step-by-step solution

To determine if a number is rational or irrational, we check if it can be expressed as a simple fraction of two integers.

A rational number can be written as (p)/(q), where p and q are integers and q ≠ 0.

An irrational number cannot be expressed as a simple fraction of two integers.

The number in question is √(23).

The integers closest to √(23) are 4 (since 4² = 16) and 5 (since 5² = 25).

Because 23 is not a perfect square, its square root, √(23), will result in a decimal that goes on forever without repeating.

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