Q&A for How to Tell if a Number Is Rational or Irrational

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Is root 225 rational or irrational?

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The square root of 225 is exactly equal to 15, therefore the root of 225 is a rational number.

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Is 0.118 a rational number?

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That is a rational number, because it can be converted into the ratio 118/1000.

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Is the square root of 41 a rational number?

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No. It is irrational because it is a decimal that cannot be precisely expressed as a fraction (that is, a ratio of two integers). Decimals that go on forever without repeating are not rational.

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Is -2/9 a rational number?

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Yes. Any number that can be expressed as the ratio of two (positive or negative) whole numbers is rational.

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Is 6/23 divided by 15/127 irrational or rational?

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It's rational. (6/23) ÷ (15/127) = (6/23)(127/15) = 762/345. Since that's the ratio of two whole numbers, it's a rational number.

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Is 49 an irrational number?

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No. 49 is a rational number, because it can be written as the fraction -- or ratio -- 49/1. (It doesn't have to be written that way. It's just that it can be written that way.)

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Is x^2 - 33 a rational number?

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It depends on what x equals. If x is a rational number or the square root of a rational number, (x² - 33) is rational.

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Is the square root of negative 27 an irrational number?

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No. It's an "imaginary" number. It is expressed as "3i√3". (It's "imaginary" because there is no "real" number that can be squared to arrive at -27.)

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