Answer:
A ⇒ rational
B ⇒ irrational
C ⇒ rational
D ⇒ rational
E ⇒ rational
F ⇒ irrational
G ⇒ rational
Step-by-step explanation:
* Lets explain what is the rational and irrational numbers
- A number is rational if we can write it as a fraction where the top
number of the fraction (numerator) and bottom number (denominator)
are both whole numbers.
- Ex: 0 , 2 , 13/7 , 0.245 , 0.33333 (repeated decimal)
- An irrational number is any number that is not rational.
- It is a number that cannot be written as a ratio of two integers
- An irrational number can be written as a decimal, but not as a fraction
- An irrational number has endless non-repeating digits to the right of
the decimal point
- Ex: √5 , π , √2/4 , 5/√7
* Lets solve the problem
# A ⇒ 11/3
∵ 11/3 is a fraction and 11 , 3 are integers
∴ 11/3 is a rational number
* A ⇒ rational
# B ⇒ √48
∵ The simplest form of √48 is 4√3
∵ √3 is an irrational number
∴ 4√3 is also an irrational number
* B ⇒ irrational
# C ⇒ 6.25
∵ 6.25 an be written as 625/100 where 625 and 100 are integers
∴ 6.25 is rational number
* C ⇒ rational
# D ⇒ 0.01045
∵ 0.01045 an be written as 1045/100000 where 1045 and 100000
are integers
∴ 0.01045 is rational number
* D ⇒ rational
# E ⇒ √(16/81)
∵ √16 = 4 and √81 = 9
∴ √(16/81) = √16/√81 = 4/9
∵ 4/9 is a fraction and 4 , 9 are integers
∴ √(16/81) is rational number
* E ⇒ rational
# F ⇒ √(3/16)
∵ √16 = 4
∴ √(3/16) = √3/√16 = √3/4
∵ √3 is an irrational number
∴ √3/4 is also irrational number
∴ √(3/16) is irrational number
* F ⇒ irrational
# G ⇒ 0.42 and a line over 42
∵ The line over 42 means 42 is repeated
∵ The repeated decimals are rational number
∴ 0.42 and line over 42 is rational number
* G ⇒ rational
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