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Worksheet: The Set of Irrational Numbers

Q1:

Find the solution set of 3 π‘₯ 7 = 3 2 in β„š β€² .

  • A  βˆ’ ο„ž 1 7 , ο„ž 1 7 
  • B { βˆ’ 7 , 7 }
  • C  βˆ’ ο„ž 9 7 , ο„ž 9 7 
  • D  βˆ’ √ 7 , √ 7 
  • E  βˆ’ 9 7 , 9 7 

Q2:

Find the solution set of 8 π‘₯ 5 = 3 2 in β„š β€² .

  • A  βˆ’ ο„ž 8 1 5 , ο„ž 8 1 5 
  • B  βˆ’ 1 5 8 , 1 5 8 
  • C  βˆ’ ο„ž 2 4 5 , ο„ž 2 4 5 
  • D  βˆ’ ο„ž 1 5 8 , ο„ž 1 5 8 
  • E  βˆ’ 2 4 5 , 2 4 5 

Q3:

Is 1 2 a rational or an irrational number?

  • Aa rational number
  • Ban irrational number

Q4:

What type of number is √ 3 2 ?

  • AInteger
  • BRational
  • CIrrational

Q5:

Is 0 . 4 5 6 a rational or an irrational number?

  • Aa rational number
  • Ban irrational number

Q6:

Given that π‘₯ = √ 8 0 + 7 8 and 𝑦 = √ 2 1 5 + 3 7  , which of the following is a good estimate of the value of π‘₯ + 𝑦 ?

  • A44
  • B56
  • C131
  • D130
  • E129

Q7:

What type of number is 1 2 ? Select all that apply.

  • Airrational
  • Binteger
  • Crational

Q8:

Is 0 . 4 a rational or an irrational number?

  • Aa rational number
  • Ban irrational number

Q9:

Given that π‘₯ = √ 8 βˆ’ 1 0 and 𝑦 = √ 1 5 + 9 , which of the following is a good estimate of the value of π‘₯ 𝑦 ?

  • A βˆ’ 9 6
  • B βˆ’ 7 8
  • C18
  • D βˆ’ 9 1

Q10:

What type of number is √ 2 ? Select all that apply.

  • Ainteger
  • Brational
  • Cirrational

Q11:

Is πœ‹ a rational or an irrational number?

  • Aan irrational number
  • Ba rational number

Q12:

Find the value of π‘₯ which satisfies the following equation βˆ’ 0 . 3 π‘₯ = 4 8 3 , given that π‘₯ is in β„š β€² .

  • A 3 √ 1 6 0
  • B βˆ…
  • C 3 ο„ž 1 1 6 0
  • D βˆ’ √ 1 6 0 3
  • E βˆ’ ο„ž 1 1 6 0 3

Q13:

Without using a calculator, order the numbers πœ‹ , √ 2 , 1, 2, and √ 3 from smallest to largest.

  • A1, √ 2 , 2, √ 3 , πœ‹
  • B πœ‹ , 2, √ 3 , √ 2 , 1
  • C πœ‹ , √ 3 , 2, √ 2 , 1
  • D1, √ 2 , √ 3 , 2, πœ‹
  • E √ 2 , 1, √ 3 , 2, πœ‹

Q14:

Benjamin wants to estimate the value of πœ‹ 2 . He knows that πœ‹ is 3.14 to two decimal places but decides to round this to the nearest whole number to make this estimate easier to calculate.

What will his estimate of πœ‹ 2 be?

Benjamin wants to check whether his approximation is accurate to the nearest whole number, so he rounds πœ‹ to 3.1. What will his approximation of πœ‹ 2 be now?

Hence, what is an approximation of πœ‹ 2 accurate to the nearest whole number?

Q15:

All integers are numbers.

  • A rational
  • B irrational

Q16:

Is √ 2 a rational or an irrational number?

  • Aan irrational number
  • Ba rational number

Q17:

According to the US Mint, the diameter of a quarter is 0.955 inches. The circumference of the quarter would be the diameter multiplied by πœ‹ . Is the circumference of a quarter a whole number, a rational number, or an irrational number?

  • Arational number
  • Bwhole number
  • Cirrational number

Q18:

On the number line, which arrow represents the value of πœ‹ ?

  • A c
  • B b
  • C a

Q19:

What type of number is πœ‹ ? Select all that apply.

  • Ainteger
  • Brational
  • Cirrational

Q20:

Is 7 a rational or an irrational number?

  • Aa rational number
  • Ban irrational number

Q21:

Without using a calculator, order the numbers βˆ’ 4 πœ‹ , βˆ’ 4 √ 3 , πœ‹ , 1 2 2 and βˆ’ 3 √ 4 from smallest to largest.

  • A βˆ’ 4 πœ‹ , βˆ’ 3 √ 4 , βˆ’ 4 √ 3 , πœ‹ 2 , 12
  • B 12, πœ‹ 2 , βˆ’ 4 √ 3 , βˆ’ 3 √ 4 , βˆ’ 4 πœ‹
  • C βˆ’ 3 √ 4 , βˆ’ 4 √ 3 , πœ‹ 2 , 12, βˆ’ 4 πœ‹
  • D βˆ’ 4 πœ‹ , βˆ’ 4 √ 3 , βˆ’ 3 √ 4 , πœ‹ 2 , 12
  • E βˆ’ 4 πœ‹ , βˆ’ 4 √ 3 , βˆ’ 3 √ 4 , 12, πœ‹ 2

Q22:

Is 𝑒 a rational or an irrational number?

  • Aan irrational number
  • Ba rational number

Q23:

I have a number that cannot be expressed in the form π‘Ž 𝑏 where π‘Ž , 𝑏 ∈ β„€ and 𝑏 β‰  0 . Is this number rational or irrational?

  • A irrational number
  • B rational number

Q24:

Without using a calculator, order the numbers 8, 7, and √ 6 6 from smallest to largest.

  • A 7 , √ 6 6 , 8
  • B √ 6 6 , 8 , 7
  • C 8 , √ 6 6 , 7
  • D 7 , 8 , √ 6 6
  • E √ 6 6 , 7 , 8