"Quadratic Radical Formula and Its Properties" PPT courseware

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"Quadratic Radical Formula and Its Properties" PPT courseware

situational navigation

The first manned spacecraft "Shenzhou 5" independently developed by my country was successfully launched on October 15, 2003.

(1) To use a launch vehicle to launch a spacecraft, the rocket must reach a certain speed in order to overcome the gravity of the earth's center and send the spacecraft into an orbit around the earth. This speed is called the first cosmic speed. The calculation formula for the first cosmic velocity is V1=√gR. Where g≈9.8 meters/second2, R is the radius of the earth. Can you find the first cosmic velocity?

(2) The speed required for a spacecraft to escape the gravity of the earth and enter an orbit around the sun is called the second cosmic speed. The speed of the second universe is V2=√2V1. What is the speed of the second universe?

communication and discovery

Shanqing Forest Farm has four square nurseries A, B, C and D. It is known that the area of ​​nursery A is S square meters.

(1) If the area of ​​nursery B is 25 square meters larger than that of nursery A, what is the side length of nursery B?

(2) If the area of ​​nursery C is twice that of nursery A, what is the side length of nursery C?

(3) If the area of ​​nursery D is 1/p of the area of ​​nursery A, what is the side length of nursery D?

(4) What common characteristics do you find in the answers to the above questions? What do they have in common with the arithmetic square roots and so on that they have learned? Communicate with classmates.

Knowledge point 1: Quadratic radicals

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

Among them, a is an integer or fraction, and a is called the radical form.

think:

If √x+2 is a quadratic radical, what conditions does the letter x need to meet?

Emphasis: To ensure that the quadratic radical is meaningful, the number under the radical must be greater than or equal to 0.

Knowledge point 2 Properties of quadratic radicals

1.a≥0, √a≥0

(double non-negativity)

Example 3: Given (x+2)2 +√y=0, find xy=?

Solution: ∵ (x+2)2 ≥0, √y≥0, (x+2)2+√y=0

∴ (x+2 )2 =0，√y=0

Solve to get x=-2 y=0

∴xy =(-2)0=1

Knowledge point 3. Inverse use of the property formula (√a)²=a(a≥0)

Reverse the formula (√a)²=a(a≥0), and you get

a=(√a)²(a≥0)

Using this formula, any non-negative number can be written as the square of a number.

Class summary

(1) The concept of quadratic radicals

(2) Properties of quadratic radicals

① a≥0, √a≥0

②(√a)²=a(a≥0)

Keywords: quadratic radicals and its properties teaching courseware, Qingdao edition eighth grade mathematics volume 2 PPT courseware download, eighth grade mathematics slide courseware download, quadratic radicals and its properties PPT courseware download, .PPT format;

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Update Time: 2024-10-18

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

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