Pregunta
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Which of the following is an irrational number?

Ask by Schwartz Ortega. in the United States
Feb 28,2025

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An irrational number is a number that cannot be expressed as a simple fraction. A common example is √2.

Solución

It looks like the answer choices for your question weren’t provided. However, one common example of an irrational number is √2 (the square root of 2). An irrational number is one that cannot be expressed as a ratio of two integers. The number √2 is proven to be irrational because if you assume that it can be written as a fraction a/b (with a and b having no common factors), you eventually end up with a contradiction involving the factorization of 2. In many multiple‐choice questions, you might see options like:  A) 2/3  B) √2  C) 5  D) 0.75 In that case, the irrational number is √2. If you have a different set of choices or need further clarification, please let me know!

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The Deep Dive

An example of an irrational number is the square root of 2 (√2), which is approximately 1.41421356 and continues infinitely without repeating. This number cannot be expressed as a simple fraction of two integers, making it irrational. It's famously known as the length of the diagonal of a square whose sides are each one unit long! Another well-known irrational number is π (pi), which represents the ratio of a circle's circumference to its diameter. Its decimal expansion starts with 3.14159 and goes on forever without repeating. Not only is π essential in geometry, but it also pops up in various areas of mathematics, physics, and engineering, making it super useful in the real world!

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