anonymous
  • anonymous
Which expression is rational? 6.27316543222718… square root of 2 square root of 14. square root of 49
Mathematics
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anonymous
  • anonymous
Which expression is rational? 6.27316543222718… square root of 2 square root of 14. square root of 49
Mathematics
schrodinger
  • schrodinger
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
Michele_Laino
  • Michele_Laino
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: \[\Large \sqrt {49} = 7 = \frac{7}{1}\]
Michele_Laino
  • Michele_Laino
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: \[\Large R = \frac{m}{n},\quad m,n \in \mathbb{Z},\;n \ne 0\]

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Michele_Laino
  • Michele_Laino
\( \Large \sqrt 2 ,\quad \sqrt {14} \) are not expressible like a ratio above
anonymous
  • anonymous
but they both can be rational
Michele_Laino
  • Michele_Laino
whereas: \[\Large \sqrt {49} = 7 = \frac{7}{1}\] is expressible as a ratio between 7 and 1
Michele_Laino
  • Michele_Laino
no, \( \large \sqrt 2 ,\quad \sqrt {14} \) are both irrational
anonymous
  • anonymous
oh
anonymous
  • anonymous
oh i see they cant be expressed as a fraction
Michele_Laino
  • Michele_Laino
yes! So what is the right option?
anonymous
  • anonymous
\[\sqrt{49}\]
Michele_Laino
  • Michele_Laino
that's right!

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