"Quadratic Radical Formula" PPT Courseware 3

Description

"Quadratic Radical Formula" PPT Courseware 3

1. Properties of square roots:

Positive numbers have two square roots and are opposites of each other;

0 has a square root which is 0;

Negative numbers have no square roots.

Think Think

1. What is the square root of 16? What is the arithmetic square root of 16?

2. What is the square root of 0? What is the arithmetic square root of 0?

3. Does -7 have a square root? Is there any arithmetic for square roots?

Both positive numbers and 0 have arithmetic square roots; negative numbers do not have arithmetic square roots.

1. The concept of quadratic radicals

√a (a≥0) represents the arithmetic square root of a non-negative number a. The formula in the form of √a (a≥0) is called a quadratic root.

It must have the following characteristics:

1. The root index is 2;

2. The radicand number must be a non-negative number.

Properties of quadratic radicals (1)

The arithmetic square root of a nonnegative number is still nonnegative.

Property 1: a ≥ 0 (a ≥ 0) (double non-negativity)

Example: |a-1|+(b+2) 2=0, then a= b=

Class summary

1. What is a quadratic radical?

2. What are the two formal characteristics of quadratic radicals?

3. What are the properties of quadratic radicals?

Property 1: √a ≥0 (a≥0) (double non-negativity)

Property 2: (√a )2 = a (a≥0)

Property 3: When a≥0, √a2 = a;

When a<0, √a2 = -a.

That is to say: √a2 = |a| .

The courseware contains a wealth of examples, fully explains the definition and properties of quadratic radicals, and strengthens difficult and key content. It is very suitable for junior high school mathematics teaching.

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For more information about the "Quadratic Radicals" PPT courseware, please click the Quadratic Radicals ppt tab.

"Mixed Operations of Quadratic Radicals" PPT courseware:

"Mixed Operations of Quadratic Radicals" PPT courseware What characteristics do they have to be combined in order to perform addition and subtraction operations of quadratic radicals? (1) Name three quadratic radicals of the same kind for 25; (2) Try to name a group of quadratic radicals of the same kind. (3) Which of the following formulas are quadratic radicals of the same kind?

"Addition and Subtraction Operations of Quadratic Radicals" PPT courseware:

"Addition and Subtraction Operations of Quadratic Radicals" PPT courseware Steps: Step 1: Convert each quadratic radical into the simplest quadratic radical. Step 2: Combine the quadratic radicals that can be combined. Summary: For quadratic radicals like 3, 12, and 75, after simplification, we use the square root of...

"Multiplication and Division Operations of Quadratic Radicals" PPT courseware:

"Multiplication and Division Operations of Quadratic Radicals" PPT courseware summary: 1. ab = ab (a0, b0) 2. a/b = a/b (or ab = ab) (a0, b>0) Note: Quadratic radicals The result of the operation should be reduced to the simplest quadratic radical. Removing the quadratic radical from the denominator is called rationalization of the denominator. Now...

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Update Time: 2024-11-20

This template belongs to Mathematics courseware People's Education Press Eighth Grade Mathematics Volume 2 industry PPT template

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