"Cube Root" PPT courseware

"Cube Root" PPT courseware

【learning target】

1. Understand the concept of cube roots and be able to use the radical sign to represent the cube root of a number;

2. Able to learn cube roots and cube root operations by analogy with square roots, and distinguish the difference between cube roots and square roots.

[Key Points] The concept and method of finding cube roots.

[Difficulty] The difference between cube roots and square roots

Take a test:

1. The arithmetic square root of 64 is ( )

2. The square root of (-6)² is ( )

3. If there is only one square root of a, then a=()

4. If one square root of the number b is 1.2, then the other square root of b is ( )

5. Arithmetic square root of √81 ( )

Collaborative exploration, display and exchange:

Exploration Activity Task 1: Understand the concept of cube roots

Read page 64 of the textbook and solve the following questions.

1.What is the cube root of a? How to describe the cube root of a using a formula?

If the cube of a number is equal to a, the number is called _____ of a. (or _____). In other words, if _____, then x is called the cube root or cubic root of a.

Recorded as: _____. Read as "_____", where a is _____, 3 is _____, and the root exponent 3_____ is omitted (fill in whether it can or not), otherwise it will be confused with the square root.

2. What is cube extraction? How does it relate to the cube?

3. Problem exchange:

⑴Exchange tutorials, appreciate the beauty of other people’s work, and discover the shortcomings of yourself and others.

⑵The group leader organizes the students in the group to talk about their confusions, and then summarizes the problems and some findings that cannot be solved in the group,

Show improvement (show unsolvable problems, accept tasks, and the team is ready!)

(Can you tell the difference between the square root of a number and the cube root of a number?)

Class summary

①The concept and properties of cube roots.

②What are the similarities and differences between cube roots and square roots? (Consider it from the definition, the number of roots, the representation method and the value range of the radicand.)

Method induction: Find the cube root of a number based on the reciprocal relationship between exponentiation and square root.

Compliance in class:

1. Determine whether it is true or false:

(1), the cube root of 25 is 5; ( )

(2) For two numbers that are opposite to each other, their cube roots are also opposite to each other; ( )

(3). There is only one cube root of any number; ( )

(4) If the square root of a number is the same as its cube root, then the number is 1; ( )

(5). If the cube root of a number is the number itself, then the number must be zero; ( )

(6). The cube root of a number is either a positive number or a negative number. ( )

(7), –64 has no cube root. ( )

2. Fill in the blanks:

(1)The square root of 64 is _______ and the cube root is _______.

(2) The cube root of ³√27 is _______; ³√-27 is the cube root of ______.

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