Question

k. $sqrt{\frac{9}{16}}$ l. $sqrt3{- 125}$ 8. circle all values that are rational numbers. 18 $-sqrt{75}$ $6\frac{1}{14}$ $\frac{15}{3}$ $sqrt{6}$ $sqrt3{64}$ directions: answer always, sometimes, or never. 9. natural numbers are __ integers. 10. irrational numbers are rational numbers. 11. rational numbers are real numbers. 12. square roots are __ rational numbers.

Explanation:

Step1: Recall number - set definitions

Natural numbers are positive integers starting from 1 ($1, 2, 3,\cdots$). Rational numbers are numbers that can be written as $\frac{a}{b}$ where $a,b\in\mathbb{Z}$ and $b
eq0$. Irrational numbers cannot be written as a fraction. Real numbers include both rational and irrational numbers.

Step2: Analyze each statement

• Statement 9: Natural numbers ($1,2,3,\cdots$) can be written as $\frac{n}{1}$ ($n\in\mathbb{N}$), so natural numbers are always rational numbers.
• Statement 10: Irrational numbers are part of the real - number system, so irrational numbers are always real numbers.
• Statement 11: Rational numbers are always rational numbers by definition.
• Statement 12: Square roots like $\sqrt{4} = 2$ (rational) and $\sqrt{2}$ (irrational), so square roots are sometimes rational numbers.

Answer:

1. always
2. always
3. always
4. sometimes