Worksheet: The Set of Irrational Numbers

In this worksheet, we will practice identifying irrational numbers and solving problems on the set of irrational numbers.

Q1:

Find the solution set of 3 𝑥 7 = 3 2 in .

  • A 1 7 , 1 7
  • B { 7 , 7 }
  • C 9 7 , 9 7
  • D 7 , 7
  • E 9 7 , 9 7

Q2:

Is 𝜋 a rational or an irrational number?

  • Aan irrational number
  • Ba rational number

Q3:

What type of number is 3 2 ?

  • AInteger
  • BRational
  • CIrrational

Q4:

Is a rational or an irrational number?

  • Aa rational number
  • Ban irrational number

Q5:

All integers are numbers.

  • A rational
  • B irrational

Q6:

I have a number that cannot be expressed in the form 𝑎 𝑏 where 𝑎 , 𝑏 and 𝑏 0 . Is this number rational or irrational?

  • A irrational number
  • B rational number

Q7:

Is 7 a rational or an irrational number?

  • Aa rational number
  • Ban irrational number

Q8:

Is 1 2 a rational or an irrational number?

  • Aa rational number
  • Ban irrational number

Q9:

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 . Is the circumference of a quarter a whole number, a rational number, or an irrational number?

  • Arational number
  • Bwhole number
  • Cirrational number

Q10:

Find the value of 𝑥 which satisfies the following equation 0 . 3 𝑥 = 4 8 3 , given that 𝑥 is in .

  • A 3 1 6 0
  • B
  • C 3 1 1 6 0
  • D 1 6 0 3
  • E 1 1 6 0 3

Q11:

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

  • Airrational
  • Binteger
  • Crational

Q12:

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

  • Ainteger
  • Brational
  • Cirrational

Q13:

Is 2 a rational or an irrational number?

  • Aan irrational number
  • Ba rational number

Q14:

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

  • Ainteger
  • Brational
  • Cirrational

Q15:

Is 𝑒 a rational or an irrational number?

  • Aan irrational number
  • Ba rational number

Q16:

Is a rational or an irrational number?

  • Aa rational number
  • Ban irrational number

Q17:

Without using a calculator, order the numbers 4 𝜋 , 4 3 , 𝜋 , 1 2 2 and 3 4 from smallest to largest.

  • A 4 𝜋 , 3 4 , 4 3 , 𝜋 2 , 12
  • B 12, 𝜋 2 , 4 3 , 3 4 , 4 𝜋
  • C 3 4 , 4 3 , 𝜋 2 , 12, 4 𝜋
  • D 4 𝜋 , 4 3 , 3 4 , 𝜋 2 , 12
  • E 4 𝜋 , 4 3 , 3 4 , 12, 𝜋 2

Q18:

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

Q19:

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

  • A c
  • B b
  • C a

Q20:

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?

Q21:

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

  • A1, 2 , 2, 3 , 𝜋
  • B 𝜋 , 2, 3 , 2 , 1
  • C 𝜋 , 3 , 2, 2 , 1
  • D1, 2 , 3 , 2, 𝜋
  • E 2 , 1, 3 , 2, 𝜋

Q22:

Given that 𝑥 = 8 0 + 7 8 and 𝑦 = 2 1 5 + 3 7 , which of the following is a good estimate of the value of 𝑥 + 𝑦 ?

  • A44
  • B56
  • C131
  • D130
  • E129

Q23:

Given that 𝑥 = 8 1 0 and 𝑦 = 1 5 + 9 , which of the following is a good estimate of the value of 𝑥 𝑦 ?

  • A 9 6
  • B 7 8
  • C18
  • D 9 1

Q24:

Find the solution set of 8 𝑥 5 = 3 2 in .

  • A 8 1 5 , 8 1 5
  • B 1 5 8 , 1 5 8
  • C 2 4 5 , 2 4 5
  • D 1 5 8 , 1 5 8
  • E 2 4 5 , 2 4 5

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