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Classify the following numbers as either rational or irrational:\newline78,16,π \frac{7}{8}, \sqrt{16}, \pi

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Full solution

Q. Classify the following numbers as either rational or irrational:\newline78,16,π \frac{7}{8}, \sqrt{16}, \pi
  1. Check Rationality of 78\frac{7}{8}:\newline Check if 78\frac{7}{8} is rational or irrational.\newline78\frac{7}{8} is a fraction of two integers. So, it is a rational number.
  2. Check Rationality of 16\sqrt{16}:\newline Check if 16\sqrt{16} is rational or irrational.\newline16=4\sqrt{16} = 4 because 42=164^2 = 16.\newline16\sqrt{16} has a perfect square, so it is a rational number.
  3. Check Rationality of π\pi:\newline Check if π\pi is rational or irrational.\newlineπ\pi is a non-repeating, non-terminating decimal. So, it is an irrational number.

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