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Is 3343 a surd or a rational number?

User Ziad Alame
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Final answer:

The number 3343 is a rational number because it is an integer and can be expressed as a fraction with an integer numerator and a denominator of one, such as 3343/1. Surds refer to irrational numbers, which 3343 is not.

Step-by-step explanation:

The number 3343 is an integer, and by definition, all integers are rational numbers. Therefore, 3343 is not a surd. A surd is a term used to describe an irrational number that cannot be expressed as a fraction of two integers, typically involving square roots of non-square numbers or other such root extractions that do not result in an integer. For example, the square root of 2 is a surd because it cannot be precisely expressed as a fraction. However, 3343 can be written as a fraction with a denominator of one, as in 3343/1, which fits the definition of a rational number. When dealing with expressions like 3¹.⁷ mentioned in your question, which seems to be referring to non-integer powers, we are entering a different realm of mathematics that often results in irrational numbers. But this does not affect the classification of the integer 3343.

User Zonabi
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