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# Unit 7: Module 7: Introduction to irrational numbers using geometry

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## About this unit

"By Module 7 students have been using the Pythagorean Theorem for several months. They are sufficiently prepared to learn and explain a proof of the theorem on their own. The Pythagorean Theorem is also used to motivate a discussion of irrational square roots (irrational cube roots are introduced via volume of a sphere). Thus, as the year began with looking at the number system, so it concludes with students understanding irrational numbers and ways to represent them (radicals, non-repeating decimal expansions) on the real number line. " Eureka Math/EngageNY (c) 2015 GreatMinds.org### Learn

### Practice

- Square rootsGet 5 of 7 questions to level up!
- Cube rootsGet 5 of 7 questions to level up!
- Equations with square roots & cube rootsGet 3 of 4 questions to level up!
- Roots of decimals & fractionsGet 3 of 4 questions to level up!
- Equations with square roots: decimals & fractionsGet 3 of 4 questions to level up!
- Square and cube challengeGet 3 of 4 questions to level up!
- Classify numbers: rational & irrationalGet 5 of 7 questions to level up!
- Classify numbersGet 5 of 7 questions to level up!
- Approximating square rootsGet 3 of 4 questions to level up!

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### Practice

- Writing fractions as repeating decimalsGet 5 of 7 questions to level up!
- Converting repeating decimals to fractionsGet 5 of 7 questions to level up!
- Converting multi-digit repeating decimals to fractionsGet 3 of 4 questions to level up!
- Comparing irrational numbersGet 5 of 7 questions to level up!
- Comparing irrational numbers with a calculatorGet 5 of 7 questions to level up!

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### Practice

- Distance between two pointsGet 5 of 7 questions to level up!
- Use Pythagorean theorem to find perimeterGet 3 of 4 questions to level up!
- Pythagorean theorem word problemsGet 3 of 4 questions to level up!
- Pythagorean theorem in 3DGet 3 of 4 questions to level up!

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### Practice

- Volume of spheresGet 3 of 4 questions to level up!
- Volume of conesGet 3 of 4 questions to level up!
- Apply volume of solidsGet 3 of 4 questions to level up!

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