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There is no such number. Between any two Irrational Numbers there are infinitely many irrational numbers. So, the claim that x is the irrational number closest to ten can be demolished by the fact that there are infinitely many irrational numbers between x and 10 (or 10 and x).

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Q: What irrational number is closest to 10?

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e, √8, pi, √10

6.000........

A non-zero rational number (10) multiplied by an irrational number (pi) is always irrational.

No

No. An irrational number is one that cannot be written as a fraction. 20/2 is a fraction that equals 10, so 10 is rational. √10 would be irrational, though.■

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The set of irrational numbers is infinitely dense. As a result there are infinitely many irrational numbers between any two numbers. So, if any irrational number, x, laid claim to be the closest irrational number to 3, it is possible to find infinitely many irrational numbers between x and 3. Consequently, the claim cannot be valid.

First - 50 is a rational number, not an irrational number since it can be represented as a ratio of integers, i.e. 50/1 With that said: the two integers closest to it are 49 and 51

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Any number that can be expressed as a fraction is a rational number otherwise it is an irrational number.

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They are the integer part of the irrational number and the successor to that integer. Thus, for pi, the two integers are 3 and 4.

The square root of any non-perfect square is an irrational number. Since sqrt(1000) = 10 sqrt(10), it is irrational.

Rational.

10

It depends on the base, but for either e or 10, it is irrational.

Irrational numbers are infinitely dense. Between any two numbers, there are infinitely many irrational numbers. So if it was claimed that some irrational, x, was the closest irrational to 6, it is possible to find an infinite number of irrationals between 6 and x. Each one of these infinite number of irrationals would be closer to 6 than x. So the search for the nearest irrational must fail.

10 is a rational number because it can be expressed as a fraction

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10+0.01 = 10.01 and it is a rational number

It is irrational because it can't be expressed as a fraction.

The result would be an irrational number

Sure; for example, 10 + pi is irrational, 10 - pi is irrational. Both are positive. If you add them, you get 20.