$$ \qquad $$ 13. Which is an irrational number? $$ \qquad $$ 14. The number 5.3456435... is: A $$ \sqrt{5} $$ B $$ \sqrt{9} $$ C -1 D $$ -\frac{2}{3} $$ A Rational B Irrational C Both D Neither $$ \qquad $$ 15. Which of the following is an $$ \qquad $$ 16. Which is a rational number? irrational number? A $$ \sqrt{144} $$ B $$ \sqrt{16} $$ A $$ \frac{3}{4} $$ B $$ \sqrt{8} $$ C $$ \sqrt{4} $$ D $$ \sqrt{3} $$ C 3.14159265... D $$ \sqrt{38} $$ 17) Which of the following numbers is irrational? a) 0.252525 ... b) 0.875 c) $$ 0.3754152 \ldots $$ d) $$ -0.121212 \ldots $$ 18) Which of the following numbers is rational? a) $$ \sqrt{30} $$ b) $$ \sqrt{42} $$ c) $$ \sqrt{64} $$ d) $$ -0.125374 \ldots $$

Question

UpStudy AI · Accepted Answer

1. For question 13, we check each option:

- Option A: $$ \sqrt{5} $$. Since 5 is not a perfect square, $$ \sqrt{5} $$ is irrational.
- Option B: $$ \sqrt{9} = 3 $$ (rational).
- Option C: $$-1$$ (rational).
- Option D: $$-\frac{2}{3}$$ (rational).

Thus, the irrational number is  
  $$ \sqrt{5} $$.

2. For question 14, the number given is  
  $$ 5.3456435\ldots $$.

A decimal that eventually repeats is a rational number. (When a block of digits repeats indefinitely, the number can be expressed as a fraction.)

Therefore, the number is Rational.

3. For question 15, the options are:

- Option A: $$ \sqrt{144} = 12 $$ (rational).
- Option B: $$ \sqrt{16} = 4 $$ (rational).
- Option C: $$ \sqrt{4} = 2 $$ (rational).
- Option D: $$ \sqrt{3} $$ is irrational because 3 is not a perfect square.

Thus, the irrational number is  
  $$ \sqrt{3} $$.

4. For question 16, the options are:

- Option A: $$ \frac{3}{4} $$ (rational).
- Option B: $$ \sqrt{8} = 2\sqrt{2} $$ (irrational).
- Option C: The decimal $$ 3.14159265\ldots $$ (if it represents $$\pi$$, it is irrational).
- Option D: $$ \sqrt{38} $$ (irrational).

Thus, the rational number is  
  $$ \frac{3}{4} $$.

5. For question 17, the options are:

- Option a) $$ 0.252525\ldots $$ is a repeating decimal, so it is rational.
- Option b) $$ 0.875 $$ is terminating, so it is rational.
- Option c) $$ 0.3754152\ldots $$ shows no clear repeating pattern, so it is irrational.
- Option d) $$ -0.121212\ldots $$ is repeating (12 repeating), hence rational.

Thus, the irrational number is  
  $$ 0.3754152\ldots $$.

6. For question 18, the options are:

- Option a) $$ \sqrt{30} $$ is irrational.
- Option b) $$ \sqrt{42} $$ is irrational.
- Option c) $$ \sqrt{64} = 8 $$ is a perfect square and is rational.
- Option d) $$ -0.125374\ldots $$ (with non-repeating decimals) is irrational.

Thus, the rational number is  
  $$ \sqrt{64} $$.
1. $$ \sqrt{5} $$ is an irrational number. 2. The number $$ 5.3456435\ldots $$ is Rational. 3. $$ \sqrt{3} $$ is an irrational number. 4. $$ \frac{3}{4} $$ is a rational number. 5. $$ 0.3754152\ldots $$ is an irrational number. 6. $$ \sqrt{64} $$ is a rational number.

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