1. Decide whether the following numbers are rational or irrational numbers: \( \sqrt{25} ;-65,2 ;-\sqrt{81} ; \frac{22}{7} ; 3,14 ; \pi ; 3 \sqrt{15} ; \sqrt[3]{-27} \) 2. Given the list of numbers \( -7,7 ; 5 ; \sqrt{-6} ; 8 ; \sqrt{35} ; 36 ; \frac{71}{3} \); write down: a) a prime number b) an irrational number c) a factor of 32 d) a square number e) an unreal number.

The number \( \sqrt{25} \) is rational since it equals 5; -65 is also rational; \( -\sqrt{81} \) is rational as it equals -9. The fraction \( \frac{22}{7} \) and 3.14 are rational approximations of π, but π itself is an irrational number, along with \( 3\sqrt{15} \). Lastly, \( \sqrt[3]{-27} \) is rational since it equals -3. From your second list: a) A prime number is 5. b) An irrational number is \( \sqrt{35} \). c) A factor of 32 is 8. d) A square number is 36. e) An unreal number is \( \sqrt{-6} \). Now let’s add some extra fun facts! Did you know that despite being widely used, \( \pi \) is not just any irrational number? It represents the ratio of the circumference of a circle to its diameter. This charming little constant pops up everywhere, from geometry to trigonometry and even in statistics! Another interesting tidbit: Rational numbers can be expressed as a fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \). This means that every terminating or repeating decimal can be expressed in such a way! So next time you encounter a fraction or a neat decimal, know it’s part of a larger family of numbers!