"The Simplest Quadratic Radical Expression" Quadratic Radical Expression PPT Courseware

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"The Simplest Quadratic Radical Expression" Quadratic Radical Expression PPT Courseware

The simplest quadratic radical

(1) The exponents of each factor of the radicand number are all 1.

(2) The radicand number does not contain a denominator.

The quadratic radical formula whose radicand satisfies the above two conditions is called the simplest quadratic radical formula.

Steps to simplify a quadratic radical:

1. Decompose the radicand into factors (or factors);

2. Replace the factor (formula) of the radicand number with its positive square root and move it outside the root sign.

3. Remove the denominator from the radicand number

4. When the radicand number is a mixed number or decimal, it must be converted into an improper fraction.

What did you learn from this section?

1. The concept of the simplest quadratic radical.

A quadratic radical that satisfies the following conditions is called the simplest quadratic radical.

(1) The radicand number does not contain factors or factors that can solve all squares;

(2) The radicand number does not contain a denominator.

2. How to convert a quadratic radical into the simplest quadratic radical.

(1) Decompose the radicand into factors (or factors);

(2) Replace the factor of the radicand number (formula) with its positive square root and move it outside the root sign.

(3) Remove the denominator in the radicand number

Simplify quadratic radicals

1. The radicand is the simplification of the quadratic root of an imperfect square number

Example 1 Simplify √48.

Analysis: Because, 48=16×3=42×3, therefore, according to the formula √a×√b=√ab (a≥0, b≥0), the product can be the part of a perfect square number or a square number Open it from the quadratic root to achieve the purpose of simplification.

Solution: √48＝√（16×3）＝√16×3＝√4²×3＝43.

2. The radicand is the simplified quadratic root of the fraction

Example 2 Simplify √1/125.

Analysis: Because, 125=5×5×5=5²×5, so you only need to multiply the numerator and denominator by 5.

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 PPT courseware "Quadratic Radicals and the Simplest Quadratic Radicals", please click the Quadratic Radicals ppt Simplest Quadratic Radicals ppt tab.

"The Simplest Quadratic Radical Expression" Quadratic Radical Expression PPT Courseware 2:

"The Simplest Quadratic Radical Expression" Quadratic Radical Expression PPT Courseware 2 Review Questions 1. What is the multiplication rule for quadratic radical expressions? How to express it in written language? What are the requirements for the results of operations? (1) ab = ab (a0, b0) (2) Multiplication of quadratic radicals: radicand...

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Update Time: 2024-11-15

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

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