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becca9898

  • one year ago

Is the square root of 5 rational or irrational? I want to say rational?

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  1. zepdrix
    • one year ago
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    A rational number looks like this: \(\large\rm \frac{a}{b}\) where a and b are whole numbers and b is not zero.

  2. zepdrix
    • one year ago
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    Here are a few examples of rational numbers: \(\large\rm \frac{5}{3}\) is a rational number. \(\large\rm 2\) is a rational number because I can write it as \(\large\rm \frac{2}{1}\). \(\large\rm 0\) is rational because I can write it as \(\large\rm \frac{0}{1}\).

  3. zepdrix
    • one year ago
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    \(\large\rm \sqrt{16}\) is rational because I can write it as \(\large\rm \frac{4}{1}\)

  4. zepdrix
    • one year ago
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    But \(\large\rm \sqrt{17}\) is `not` rational. There is no nice representation with integers for this number :(

  5. zepdrix
    • one year ago
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    Any ideas for the sqrt(5)? :) Does this give you any hints?

  6. becca9898
    • one year ago
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    I would say then it would be irrational because there is no representation?

  7. Hero
    • one year ago
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    The square root of a prime number is irrational

  8. becca9898
    • one year ago
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    Thank you guys!

  9. zepdrix
    • one year ago
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    Yay good job becca \c:/ Another way to think about it, only the `perfect squares` are going to be rational when placed under a root. So square root of 4, 9, 16, 25, 36 and so on... these are are rational numbers. All of the roots between them are not.

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