Irrational Numbers — Definition & Examples
Read this topicExplanations 3
- What is an Irrational Number? Irrational numbers are kind of the opposite of rational. They are [real] (https://www.expii.com/t/what-are-real-numbers-9010) numbers that we can't…
By Eunji Kwon, Jonathan Heller, Alex Federspiel, Caroline K, Joshua Siktar
- (Video) Examples of Irrational Numbers by Derek Rouch This video by Derek Rouch goes over the differences between rational and irrational numbers. Every number is either rationa…
By Eunji Kwon, Jonathan Heller, Alex Federspiel, Caroline K, Joshua Siktar
- What is an Irrational Number? Irrational numbers are not rational—they are real numbers that we cannot write as a ratio pq\frac{p}{q}qp (where ppp and qqq are integers, with q≠…
By Caroline K, Jonathan Heller, Alex Federspiel, Victor Wang, Joshua Siktar
Problems 48
- Which of the following choices are irrational numbers? Select all that apply.
- Which of the following are whole numbers?
- Which of the following are NOT rational numbers? Select all that apply.
- Which set contains all rational numbers?
- True or False\text{True or False}True or False === 3.1415926535893.1415926535893.141592653589 is irrational.
- Which of the following are rational numbers? Select all that apply.
- Which of the following are irrational numbers? Select all that apply.
- The set of irrational numbers is contained in which set?
- True or False\text{True or False}True or False === π≈227\pi\approx\frac{22}{7}π≈722 so 227\frac{22}{7}722 is an irrational number.
- Irrational numbers are closed under which of the following operations? Select all that apply.
- Is 000 an irrational number?
- Which of the following are irrational?
- True or False\text{True or False}True or False === 22n+1\sqrt{2}^{2n+1}22n+1, where nnn is any integer, is always irrational.
- Which of the following are irrational numbers? (Select all that apply.)
- Which of the following, when multiplied by a natural number, could not create an integer?
- Which of the following are not real numbers?
- Which of the following are on the real number line? Select all correct answers.
- Which of the following is true? Mark all that are correct.
- Which of the following doesn't have a real square root (as opposed to an imaginary square root)?
- Which of the following numbers are positive? Select all that apply.
- Which of the following are whole numbers?
- The set of all real numbers contains which of the following? Mark all that apply.
- Is π\piπ a real number?
- When is a fraction of real numbers definitely not rational?
- Which of the following are irrational numbers? Mark all that apply
- Is 9\sqrt{\sqrt{9}}9 irrational?
- Is 16\sqrt{\sqrt{16}}16 irrational?
- Is 9\sqrt{9}9 irrational?
- Which one of the following powers of 222 is irrational?
- Which of the following powers of 999 is irrational?
- Pi has long been noted as one of the most useful mathematical constants. Yet, due to the fact that it is an irrational number, it can never be expressed exactly as a fraction an…
- What type of number is 3\sqrt{3}3? (Mark all choices that apply.)
- Select the sets that all of the numbers above belong to.
- Select the sets that all of the numbers above belong to.
- Choose all answers that apply. A natural number is always....
- The ratio of the number of sneakers in the world to the number of feet in the world would fall under which sets?
- A switchboard assigns the value 111 to a number that's rational and 000 to a number that's irrational. AB4π3ππ2\begin{array}{c|c} \text{A}&\text{B}\\ \hline \frac{4\pi}{3\pi}&\f…
- A switchboard assigns the value 111 to a number that's rational and 000 to a number that's irrational. AB231007\begin{array}{c|c} \text{A}&\text{B}\\ \hline \frac23&\frac{100}{7…
- True or False\text{True or False}True or False === If you add an irrational number to another irrational number the result will always be an irrational number.
- True or False\text{True or False}True or False === All square roots are irrational numbers.
- True or False\text{True or False}True or False === Repeating decimals are irrational numbers.
- Select the irrational numbers.
- Select the irrational numbers.
- Select the irrational numbers.
- Select the irrational numbers.
- Is 7\sqrt{7}7 an irrational number?
- Which of the following is an irrational number?
- True or False\text{True or False}True or False === An irrational number raised to the power of an irrational number is always irrational. Hint: Try using 2\sqrt{2}2 to come up …