"Square Root" PPT Courseware 6

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"Square Root" PPT Courseware 6

1. Definition of square root

(1) Generally, if the ______ of a number is equal to a, then the number is called the square root or quadratic root of a. That is to say, if x2=a, then x is called the square root of a.

(2) The operation of finding the _______ of a number a is called the square root.

2. Properties of square roots

(1) There are two square roots of positive numbers, and they are opposites of each other.

(2)The square root of 0 is ______.

(3) The square root of a negative number ________.

Note: The connection and difference between square roots and arithmetic square roots:

Square Roots and Arithmetic Square Roots

connect

①The radicands of square roots and arithmetic square roots are both non-negative numbers.

②The square root of zero and the arithmetic square root are both zero.

the difference

① There are two square roots of a positive number a, namely ±√a, which are opposites of each other, while there is only one arithmetic square root of a positive number a, namely √a

②The value of the square root of arithmetic must be a non-negative number, but the value of the square root is not necessarily a non-negative number.

③The arithmetic square root of a positive number must be its square root, but the square root of a positive number is not necessarily its arithmetic square root.

Definition of square root (key points)

Example 1: Find the square root of each of the following numbers:

(1)36; (2)(-5)²;

(3)－(－9)³；(4)8＋(-1/6)²

Idea guide: According to the definition of square root, first determine which number whose square is equal to a. Some numbers must be simplified first and then find their square root.

Example 2: If 2m-4 and 3m-1 are the square roots of the same number, what is this number?

Idea guide: There are two square roots of a positive number, and they are opposites of each other. According to the meaning of the question, we can see that there are two situations in the relationship between 2m-4 and 3m-1, one is equal, and the other is mutually opposite. ．

Solution: When 2m-4=3m-1, m=-3,

∴(2m-4)2＝[2×(-3)-4]2＝100.

When 2m-4+3m-1=0, m=1,

∴(2m-4)2＝(2×1-4)2＝4.

So the number is 100 or 4.

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"Square Root" PPT courseware 9:

"Square Roots" PPT Courseware 9 Learning Objectives 1. Be able to tell the meaning of arithmetic square roots, and be able to use symbols to represent the arithmetic square roots of positive numbers. (Key Points) 2. Be able to use square operations to find the arithmetic square roots of certain non-negative numbers. (Key Points) 3 . Be able to understand and apply the properties of square roots in arithmetic..

"Square Root" PPT courseware 8:

"Square Root" PPT Courseware 8 [Learning Objectives] (Only when you have a goal in mind will you have a direction in learning) 1. Understand the definition of square root, master the properties of square root, and use the root sign to represent the square root of a number. 2. Know that the square root and the square are mutually exclusive The inverse operation will make use of this reciprocal operation.

"Square Root" PPT courseware 7:

"Square Root" PPT Courseware 7 Knowledge Review ⑴ The square root of 25 is 5. ⑵ The square root of 81 is 9. ⑶ The square root of 49/64 is 7/8. ⑷ The square root of 0 is 0. ⑸ Does -4 have a square root? Arithmetic square root The positive square root a of a positive number a is called the arithmetic square of a..

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Update Time: 2024-10-02

This template belongs to Mathematics courseware Hebei Education Edition Eighth Grade Mathematics Volume 1 industry PPT template

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