# Worksheet: The Set of Irrational Numbers

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

**Q2: **

Is a rational or an irrational number?

- Aan irrational number
- Ba rational number

**Q3: **

What type of number is ?

- 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 where , and . 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 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 . 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 which satisfies the following equation , given that is in .

- A
- B
- C
- D
- E

**Q11: **

What type of number is ? Select all that apply.

- Airrational
- Binteger
- Crational

**Q12: **

What type of number is ? Select all that apply.

- Ainteger
- Brational
- Cirrational

**Q13: **

Is a rational or an irrational number?

- Aan irrational number
- Ba rational number

**Q14: **

What type of number is ? Select all that apply.

- Ainteger
- Brational
- Cirrational

**Q15: **

Is 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 , , and from smallest to largest.

- A , , , , 12
- B 12, , , ,
- C , , , 12,
- D , , , , 12
- E , , , 12,

**Q18: **

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

- A
- B
- C
- D
- E

**Q19: **

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

- 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?

**Q23: **

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

- A
- B
- C18
- D