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anonymous

  • one year ago

Which expression is rational? 6.27316543222718… square root of 2 square root of 14. square root of 49

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  1. anonymous
    • one year ago
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    @Michele_Laino

  2. Michele_Laino
    • one year ago
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    hint: the first number is an number with an infinity of decimal figures, so it is an irrational number, furthermore, we have 49=7^2, so: \[\Large \sqrt {49} = 7 = \frac{7}{1}\]

  3. Michele_Laino
    • one year ago
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    hint: a rational number R, is a number which can be written as a ratio between two integers, say m, and n, and such that n is different from zero, namely: \[\Large R = \frac{m}{n},\quad m,n \in \mathbb{Z},\;n \ne 0\]

  4. Michele_Laino
    • one year ago
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    \( \Large \sqrt 2 ,\quad \sqrt {14} \) are not expressible like a ratio above

  5. anonymous
    • one year ago
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    but they both can be rational

  6. Michele_Laino
    • one year ago
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    whereas: \[\Large \sqrt {49} = 7 = \frac{7}{1}\] is expressible as a ratio between 7 and 1

  7. Michele_Laino
    • one year ago
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    no, \( \large \sqrt 2 ,\quad \sqrt {14} \) are both irrational

  8. anonymous
    • one year ago
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    oh

  9. anonymous
    • one year ago
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    oh i see they cant be expressed as a fraction

  10. Michele_Laino
    • one year ago
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    yes! So what is the right option?

  11. anonymous
    • one year ago
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    \[\sqrt{49}\]

  12. Michele_Laino
    • one year ago
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    that's right!

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