Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

In this lesson, we will learn how to solve problems on the set of irrational numbers.

Q1:

Find the solution set of 3 π₯ 7 = 3 2 in β β² .

Q2:

Find the solution set of 8 π₯ 5 = 3 2 in β β² .

Q3:

Is 1 2 a rational or an irrational number?

Q4:

What type of number is β 3 2 ?

Q5:

Is a rational or an irrational number?

Q6:

Given that π₯ = β 8 0 + 7 8 and π¦ = β 2 1 5 + 3 7 ο’ , which of the following is a good estimate of the value of π₯ + π¦ ?

Q7:

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

Q8:

Q9:

Given that π₯ = β 8 β 1 0 and π¦ = β 1 5 + 9 , which of the following is a good estimate of the value of π₯ π¦ ?

Q10:

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

Q11:

Is π a rational or an irrational number?

Q12:

Find the value of π₯ which satisfies the following equation β 0 . 3 π₯ = 4 8 3 , given that π₯ is in β β² .

Q13:

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

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.

Q16:

Is β 2 a rational or an 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 . Is the circumference of a quarter a whole number, a rational number, or an irrational number?

Q18:

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

Q19:

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

Q20:

Is 7 a rational or an irrational number?

Q21:

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

Q22:

Is π a rational or an irrational number?

Q23:

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

Q24:

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

Donβt have an account? Sign Up