"Quadratic Radical Formula" Real Numbers PPT

Description

"Quadratic Radical Formula" Real Numbers PPT

Part One: Knowledge Review

1.What is the arithmetic square root of a number? How to express?

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

The arithmetic square root of a is (a≥0), where the arithmetic square root of 0 is 0.

2.What is the square root of a number? How to express?

Generally, if the square of a number x is equal to a, that is, x2=a,

Then this number x is called the square root (or quadratic root) of a.

3. What are the 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.

Quadratic radical PPT, part 2: joint exploration

As shown in the figure, it is known that the area of ​​the square is b-3, then the side length of the square is _____.

What do you think the algebraic expressions obtained have in common?

represents the arithmetic square root of some positive number;

Generally, formulas of the form √a (a≥0) are called quadratic radicals;

a is called the radicand number.

Core summary

Generally, formulas of the form √a (a≥0) are called quadratic radicals.

1. Represents the arithmetic square root of a;

2. a can be a number or a formula;

3. The form contains the quadratic root sign √;

4. a≥0, √a≥0 (double non-negativity);

5. It can express both the square root operation and the result of the operation.

Quadratic Radical PPT, Part 3: Independent Exploration

Example 1 Let’s talk about which of the following expressions are quadratic radicals.

Example 2 Find the value range of the letters in the following quadratic root formula:

[Analysis] (1) Since the radicand is a non-negative number, it can be seen that a+1≥0, that is, a≥-1.

(2) Since the radicand is a non-negative number and the denominator is not zero, it can be seen that 1-2a>0, that is, a< .

(3) From (a-3) 2≥0, it can be seen that a can take any real number.

Quadratic radical PPT, part 4: summary

Addition and subtraction rules for quadratic radicals

Generally speaking, when adding and subtracting quadratic radicals, you can first convert the quadratic radicals into the simplest quadratic radicals, and then combine the quadratic radicals with the same radicand.

Important reminder

1. The operation steps of addition and subtraction: "one, simplify, two, judge and three, merge".

2. Prerequisite for merging: Only the simplest quadratic radicals with the same radicand can be merged.

Keywords: Beijing Normal University edition eighth grade mathematics PPT courseware free download, quadratic radical PPT download, real number PPT download, .PPT format;

For more information about the "Quadratic Radicals of Real Numbers" PPT courseware, please click on the Real Numbers PPT Quadratic Radicals PPT tab.

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Update Time: 2024-09-06

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