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Lesson: The Set of Irrational Numbers

Sample Question Videos

Worksheet • 24 Questions • 1 Video

Q1:

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

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

Q2:

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

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

Q3:

Is 1 2 a rational or an irrational number?

  • Aan irrational number
  • Ba rational number

Q4:

What type of number is √ 3 2 ?

  • ARational
  • BIrrational
  • CInteger

Q5:

Is a rational or an irrational number?

  • Aan irrational number
  • Ba rational 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 ?

  • A130
  • B129
  • C56
  • D131
  • E44

Q7:

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

  • Ainteger
  • Brational
  • Cirrational

Q8:

Is a rational or an irrational number?

  • Aan irrational number
  • Ba rational 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 1
  • B βˆ’ 7 8
  • C18
  • D βˆ’ 9 6

Q10:

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

  • Arational
  • Birrational
  • Cinteger

Q11:

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

  • Aa rational number
  • Ban irrational 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 βˆ’ √ 1 6 0 3
  • B βˆ’ ο„ž 1 1 6 0 3
  • C βˆ…
  • D 3 ο„ž 1 1 6 0
  • E 3 √ 1 6 0

Q13:

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

  • A1, √ 2 , √ 3 , 2, πœ‹
  • B √ 2 , 1, √ 3 , 2, πœ‹
  • C πœ‹ , 2, √ 3 , √ 2 , 1
  • D πœ‹ , √ 3 , 2, √ 2 , 1
  • E1, √ 2 , 2, √ 3 , πœ‹

Q14:

Maged wants to estimate the value of . He knows that 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 be?

Maged wants to check whether his approximation is accurate to the nearest whole number, so he rounds to 3.1. What will his approximation of be now?

Hence, what is an approximation of accurate to the nearest whole number?

Q15:

All integers are numbers.

  • A irrational
  • B rational

Q16:

Is √ 2 a rational or an irrational number?

  • Aa rational number
  • Ban irrational 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?

  • Awhole number
  • Birrational number
  • Crational number

Q18:

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

  • A b
  • B a
  • C c

Q19:

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

  • Arational
  • Birrational
  • Cinteger

Q20:

Is 7 a rational or an irrational number?

  • Aan irrational number
  • Ba rational 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’ 4 √ 3 , βˆ’ 3 √ 4 , πœ‹ 2 , 12
  • B βˆ’ 4 πœ‹ , βˆ’ 4 √ 3 , βˆ’ 3 √ 4 , 12, πœ‹ 2
  • C 12, πœ‹ 2 , βˆ’ 4 √ 3 , βˆ’ 3 √ 4 , βˆ’ 4 πœ‹
  • D βˆ’ 3 √ 4 , βˆ’ 4 √ 3 , πœ‹ 2 , 12, βˆ’ 4 πœ‹
  • E βˆ’ 4 πœ‹ , βˆ’ 3 √ 4 , βˆ’ 4 √ 3 , πœ‹ 2 , 12

Q22:

Is 𝑒 a rational or an irrational number?

  • Aa rational number
  • Ban irrational 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 rational number
  • B irrational number

Q24:

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

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