Exploring Irrational Numbers - Grade 12 Math
A Grade 12 math worksheet focusing on the properties, identification, and operations involving irrational numbers, aligned with advanced number sense concepts.
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Exploring Irrational Numbers
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Read each question carefully and provide the best answer. Show all your work for full credit.
1. Which of the following numbers is irrational?
√49
0.333...
π
-5/2
2. The product of a non-zero rational number and an irrational number is always:
Rational
Irrational
Integer
Undefined
1. An irrational number cannot be expressed as a simple .
2. The decimal representation of an irrational number is non-terminating and .
3. The square root of any non-perfect square is an number.
1. The sum of two irrational numbers is always irrational.
True
False
2. Every real number is either rational or irrational.
True
False
1. Explain why √2 is an irrational number. Provide a brief proof or explanation.
2. Plot the approximate location of √5 on the number line below.
1. Discuss the implications of irrational numbers in various branches of mathematics (e.g., geometry, calculus, number theory). Provide at least two specific examples.