# Why is the square root of 5 an irrational number?

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This is a sketch of a contradiction-based proof:

Therefore, by definition:

Thus, we have:

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The square root of 5 is an irrational number because it cannot be expressed as a fraction of two integers where the denominator is not zero, and the numerator and denominator have no common factors other than 1. In other words, the decimal expansion of the square root of 5 neither terminates nor repeats in a pattern. This property is characteristic of irrational numbers.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- In the following expression, what are the third and fourth operations?: #[(8+5) (6-2) ^2] - (4*17/2)#
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- If sally has 3 out of 5 votes for first place and Jane has the other two but Carolyn has 4 votes for second place, would it go first place sally second place Jane or first place sally second place Carolyn?

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