"Square Root" PPT courseware

Description

"Square Root" PPT courseware

Review the past and learn the new

1.What is the square root of arithmetic?

Generally, if the square of a positive number x is equal to a, that is, x² =a, then this positive number x is called the arithmetic square root of a.

The arithmetic square root of a is recorded as: √a and is read as: "root a",

a is called the radicand number.

2. Determine whether the following numbers have arithmetic square roots, and if so, find their arithmetic square roots.

100;1;36/121;0;-0.0025; (-3)2-25;

3. What operations have we already learned? Which of them are the inverse operations of each other?

Answer: There are five operations: addition, subtraction, multiplication, division, and exponentiation.

Addition and subtraction are reciprocal; multiplication and division are reciprocal.

Is there any inverse operation for exponentiation?

Explore new knowledge

1. The square of a number is 9. What is this number?

2. The square of a number is 4/25. What is this number?

3. Fill in the blanks:

①( )2 = 16 ②( )2 =1/4

③ ( ) 2 = 0 ④ ( ) 2 = 0.49

Concept introduction

∵(±1.2)2=1.44 ∴ ±1.2 is called the square root of 1.44

∵(±2)2=4 ∴±2 is called the square root of 4

∵ x² = a ∴ x is called the square root of a

Generally, if the square of a number is equal to a, then the number is called the square root of a, also called the square root of a.

Solution: ∵(±7)2=49 ∴±7 is called the square root of 49

∵ (±1/5)2=1/25 ∴ ±1/5 is called the square root of 1/25

∵ 02 = 0 ∴ 0 is called the square root of 0

Think about how to express the square root of a?

What does it mean?

Properties of square roots

Give it a try:

(1)What is the square root of 144?

(2)What is the square root of 0?

(3)What is the square root of 64/121?

(4) What is the square root of -4? Why? What did you find out from the answers above?

Discuss

(1) How many square roots does a positive number have? What is their relationship?

(2) How many square roots does 0 have?

(3) What about a negative number?

A positive number a has two square roots, which are opposites of each other;

0 has only one square root, which is 0 itself;

Negative numbers have no square roots.

practise

(1) The square root of 114 is -12 and 12;

(2) The square root of 256 is 16;

(3) The square root of 0 and the arithmetic square root are both 0 ( )

(4) The square root of (-4)² is -4 ( )

(5)-5 is the square root of 25;

(6) The square root of 1 is 1;

(7) The square root of -1 is -1;

(8)-1 is the square root of 1;

(9) (-1) The square root of 2-1.

Self test:

(1) (-5) The square root of 2 is _____, and the square root of arithmetic is _____;

(2) The square root of √16 is ____, and the square root of arithmetic is _____.

(3) If x²=9, then x=____, if √x²=3, then x=_____;

(4) If (x-1)2=4, then x=_____,

(5) If one square root of a number is -7, then the other square root is _____, the number is _____.

(6) If the two square roots of a positive number are 2a-6 and 3a+1, then a=_____, and the positive number is _____;

my gains

① Understand the concepts of square roots and arithmetic square roots;

② Master the properties of square roots: a positive number has two square roots, and they are opposites of each other. The square root of 0 is 0, and a negative number has no square root;

③Learn how to express square roots and arithmetic square roots;

④ Learned to find the square root of a number and understood that the square root and the square are inverse operations of each other.

Strengthen

1. The arithmetic square root of a number is equal to itself. This number is 0 or 1.

2. If x²=16, then the arithmetic square root of 5-x is 1 or 3

3. If the square root of 4a+1 is ±5, then the arithmetic square root of a² is 6

Classroom meets standards

(1) Find the square root of each of the following numbers:

(1) 36 (2) 0.49

(3)1/4 (4)16/25

(5) 102 (6)-9

(7)(-4)2 (8)0

2. Judgment questions

1) The square root of 1.21 is ± 1.1 ( )

2) The square root of 9 is 3 ( )

3) -5 is the square root of 25 ( )

4) The square root of √16 is ± 4 ( )

5) The square root is itself a number with 0,1 ()

Class summary

1. The concept of square root

2. Square root representation method

3. Properties of square roots

4. The difference and connection between square roots and arithmetic square roots

5. Comparison of square roots

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For more information about the "Square Root" PPT courseware, please click the Square Root ppt tab.

"Square Root" PPT courseware 9:

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"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: 2024-11-24

This template belongs to Mathematics courseware Qingdao Edition Eighth Grade Mathematics Volume 2 industry PPT template

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