Irrational number

High school (ages 12+)
Mathematics & Numbers

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/irrational-number

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the decimal property?Possess infinite, non-repeating decimal expansions
2. Why were irrational numbers scary for ancient Greeks?The Greeks believed all numbers were ratios of whole numbers, so finding numbers that couldn't be expressed that way challenged their beliefs.
3. How does the square root of 2 show that numbers can be irrational?The diagonal of a unit square is √2, and no fraction can equal that length, so √2 is irrational.

Commensurable: Capable of being measured by a common unit; expressible as a ratio of integers.
Transcendental Number: An irrational number that is not a root of any non-zero polynomial equation with integer coefficients.
Real Number: Any number that can be found on the number line, including rational and irrational numbers.