# Worksheet: The Set of Irrational Numbers

Q1:

Find the solution set of in .

• A
• B
• C
• D
• E

Q2:

Find the solution set of in .

• A
• B
• C
• D
• E

Q3:

Is a rational or an irrational number?

• Aa rational number
• Ban irrational number

Q4:

What type of number is ?

• AInteger
• BRational
• CIrrational

Q5:

Is a rational or an irrational number?

• Aa rational number
• Ban irrational number

Q6:

Given that and , which of the following is a good estimate of the value of ?

• A44
• B56
• C131
• D130
• E129

Q7:

What type of number is ? Select all that apply.

• Airrational
• Binteger
• Crational

Q8:

Is a rational or an irrational number?

• Aa rational number
• Ban irrational number

Q9:

Given that and , which of the following is a good estimate of the value of ?

• A
• B
• C18
• D

Q10:

What type of number is ? Select all that apply.

• Ainteger
• Brational
• Cirrational

Q11:

Is a rational or an irrational number?

• Aan irrational number
• Ba rational number

Q12:

Find the value of which satisfies the following equation , given that is in .

• A
• B
• C
• D
• E

Q13:

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

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

Q14:

Benjamin 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?

Benjamin 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 rational
• B irrational

Q16:

Is 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 . 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 ?

• A c
• B b
• C a

Q19:

What type of number is ? 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 , , and from smallest to largest.

• A , , , , 12
• B 12, , , ,
• C , , , 12,
• D , , , , 12
• E , , , 12,

Q22:

Is a rational or an irrational number?

• Aan irrational number
• Ba rational number

Q23:

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

• A irrational number
• B rational number

Q24:

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

• A
• B
• C
• D
• E