"Addition and Subtraction of Quadratic Radicals" Quadratic Radicals PPT Courseware 4

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"Addition and Subtraction of Quadratic Radicals" Quadratic Radicals PPT Courseware 4

The concept of the simplest quadratic radical

1. A quadratic radical that satisfies what conditions is called the simplest quadratic radical?

(1) The radicand number does not contain a denominator; that is, the radicand number is an integer or an integer;

(2) The radicand number does not contain factors or factors that can solve all squares.

General steps for simplifying quadratic radicals:

Eliminate the denominator under the root sign, and replace the factors or factors in the radicand number that can be solved to all squares with their arithmetic square roots and then move them outside the root sign. When simplifying, follow the relevant properties of the quadratic root formula. .

2. Simplify the following quadratic radicals

√8 √18 √50 √45

√75 √32 √1/12 √1/2

3. Introduction of new courses

1. Two trains carry 2x tons and 3x tons of coal respectively. How much do these two trains transport in total? 2x +3x=5x(tons)

2. The two trains transport 2x tons and 3y tons of coal respectively. How much do the two trains transport in total? (2x +3y) tons

Can you calculate the following questions using the same method?

(1)3√2+4√2 (2)√5+√2

(3)√8+√18+4√2

How to determine whether a set of formulas are quadratic radicals of the same type

First convert these equations into the simplest quadratic radicals. Since their radicans are the same, they are quadratic radicals of the same type.

Note: To judge whether a set of formulas are quadratic radicals of the same type, you only need to see whether the radicands after being transformed into the simplest quadratic radical are the same, and it has nothing to do with the factors and symbols in front of the simplest quadratic formula.

Merge similar radicals

Similar quadratic radicals can also be combined. The method is similar to merging similar terms. Add and subtract coefficients or letters outside the radical sign. The root exponent and radicand remain unchanged. Therefore, we can say: to add and subtract several quadratic radicals, first add and subtract each Convert the quadratic radicals into the simplest quadratic radicals, and then merge the same quadratic radicals separately

Expansion and extension:

(1)5√2+√8-7√18

(2)√8-4/√2+√(-1)²

Steps for addition and subtraction of quadratic radicals:

(1) Convert each quadratic radical into the simplest quadratic radical;

(2) Find the same kind of quadratic radicals;

(3) Combine similar quadratic radicals.

summary

1. Similar quadratic radicals are relative to a group of quadratic radicals. To determine whether several quadratic radicals are the same kind of quadratic radicals, you must first convert these quadratic radicals into the simplest quadratic radicals, and then look at their radicans. If the radicans are the same, then the original Several quadratic radicals are quadratic radicals of the same type.

2. Similar quadratic radicals are not necessarily the simplest quadratic radicals. Such as: √2, √8, √50, etc.

3. To add and subtract several quadratic radicals, first convert each quadratic radical into the simplest quadratic radical, and then merge the same quadratic radicals respectively.

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Update Time: 2024-09-22

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

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