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Flauer [41]
3 years ago
9

Which number produces an irrational number when multiplied by 1/3

Mathematics
1 answer:
MArishka [77]3 years ago
3 0

We can simply observe that.

  1. 0.777... is rational, because it is a number with infinite but repeating decimal part.
  2. 1/3 is rational, because it's the division between two integers
  3. -\sqrt{16}=-4, so this is rational as well.

Since the product of two rational numbers is always rational, we have that

0.\bar{7}\cdot \dfrac{1}{3},\quad \dfrac{1}{3}\cdot \dfrac{1}{3},\quad -4\cdot \dfrac{1}{3}

are all rationals, since they are the product of two rationals.

On the other hand, we have

\sqrt{27}=\sqrt{9\cdot 3}=3\sqrt{3}

and thus

3\sqrt{3}\cdot \dfrac{1}{3}=\sqrt{3}

which is irrational.

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