Unit 1: The Number System & Roots · NY-8.NS.1, AI-N.RN.3
Grade 8 State Test
Notes
The two teams. Rational numbers include integers, fractions, terminating decimals, and repeating decimals. Irrational numbers include √2, √3, π, and non-repeating non-terminating decimals. Between any two rationals there are irrationals — and vice versa.
Why √2 is irrational (sketch). If √2 = a/b in lowest terms, then a² = 2b², so a is even, then b is even, which contradicts lowest terms. You do not need a formal proof for the Grade 8 test, but you must know √2, √3, π are irrational and √9 is rational.
Vocabulary
rational number: A number that can be written as a/b where a and b are integers and b ≠ 0.
irrational number: A real number that cannot be written as a ratio of integers.
Practice (no calculator unless marked)
Which statement about the value of √50 is true?
A. It is irrational because the decimal equivalent eventually repeats.
B. It is rational because the decimal equivalent eventually terminates.
C. It is rational because the value as a decimal is equivalent to a fraction.
D. It is irrational because the decimal equivalent is non-repeating and does not terminate.
Which expression represents an irrational number?
A. √16 + 1
B. √25 + 4
C. √36 + √7
D. √49 + 9
Which statement about the value of √50 is true?
A. It is irrational because the decimal equivalent eventually repeats.
B. It is rational because the decimal equivalent eventually terminates.
C. It is rational because the value as a decimal is equivalent to a fraction.
D. It is irrational because the decimal equivalent is non-repeating and does not terminate.
Which expression represents an irrational number?
A. √16 + 1
B. √25 + 4
C. √36 + √7
D. √49 + 9
Which statement about the value of √50 is true?
A. It is irrational because the decimal equivalent eventually repeats.
B. It is rational because the decimal equivalent eventually terminates.
C. It is rational because the value as a decimal is equivalent to a fraction.
D. It is irrational because the decimal equivalent is non-repeating and does not terminate.
Which expression represents an irrational number?
A. √16 + 1
B. √25 + 4
C. √36 + √7
D. √49 + 9
Which statement about the value of √50 is true?
A. It is irrational because the decimal equivalent eventually repeats.
B. It is rational because the decimal equivalent eventually terminates.
C. It is rational because the value as a decimal is equivalent to a fraction.
D. It is irrational because the decimal equivalent is non-repeating and does not terminate.