A teacher asked students to
write irrational numbers and
terminating decimal numbers on
slips The following were the
answers given by students.
sqrt 45+3 sqrt 20 4* b) 23 2^1
*5^2 c) 315 16 d) sqrt 289 15 +
2sqrt(3) 12.31245789 Answer
the following questions ) How
many are irrational numbers? )
How many are terminating
decimal numbers? iii) Sort the
numbers ander two categories. )
Write decimal expansion of the
numbers taken in part (iu)
Answers
Identified Terminating Decimal & irrational number
Step-by-step explanation:
Terminating Decimal - if Denominator has only prime factors 2 or 5
irrational number which can be written in the form of p/q where p & q are integers
sqrt 45+3 sqrt 20
√45 + 3√20
= 5√3 + 6√5
is irrational number
23/ 2¹ * 5² (Terminating Decimal)
= 0.92
315/16
= 315/2⁴ (Terminating Decimal)
= 19.6875
√289 = 17.0 ( terminating decimal)
15 + 2√3 ( irrational number)
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Step-by-step explanation:
Given A teacher asked students to write irrational numbers and terminating decimal numbers on slips The following were the answers given by students.
- So a terminating decimal is a decimal that stops and it has finite number of digits.
- Now irrational numbers are those numbers which are not represented in a fractional form that is p/q and they neither terminate nor repeat.
- So we have √45 + 3 √20
- = √9 x 5 + 3 √4 x 5
- = 3 √5 + 6√5
- = 9 √5 is an irrational number
- Now 23 / 2^1 x 5^2
- = 11.5 x 25
- = 287.5 is a terminating decimal.
- Now √315 = 17.7 is an irrational number and is not terminating
- So √289 + 2 √3
- = 17 + 2√3 is an irrational number.
Reference link will be
https://brainly.in/question/17849937