This paper summarizes the calculation method of the mixed operation of quadratic radical addition, s

Multiplication and division of quadratic radicals.

1.The property of the square root of the arithmetic product.

For example: ab= a· b(a 0, b 0).

The law of multiplication. For example: ab= a· b(a 0, b 0).

The multiplication algorithm of quadratic radicals is described in language as: the product of the arithmetic square roots of the two factors is equal to the arithmetic square roots of the products of the two factors.

3.The law of division.

a÷√b=√a÷b（a≥0，b>0）

The division operation of the quadratic root formula is described in language as: the quotient of the arithmetic square root of two numbers is equal to the arithmetic square root of the quotient of these two numbers.

4.There is a rationalized radical formula.

If the product of two algebraic formulas containing radicals no longer contains radicals, then these two algebraic expressions are called rationalized radicals, also known as rationalized factors.

The addition and subtraction of the quadratic radical formula in this paragraph.

Homogeneous quadratic radical.

Generally speaking, after several quadratic radicals are reduced to the simplest quadratic radicals, if they have the same number of squares, these quadratic radicals are called the same quadratic radicals.

Merge the same quadratic radicals.

Merging several homogeneous quadratic radicals into one quadratic radical is called merging homogeneous quadratic radicals.

3. When adding or subtracting quadratic radicals, you can first convert the quadratic radicals into the simplest quadratic radicals, and then merge the same number of squares.

For example: 2 5

Ten 5 = 3 5

4. When there are brackets, the brackets should be removed first.

When there are parentheses, the ones in the parentheses are counted first, then multiplied and divided, and finally added and subtracted.

When there are no parentheses, multiplication and division are calculated first, and addition and subtraction are calculated later.

Only when addition, subtraction or multiplication and division are calculated sequentially.

The method of addition, subtraction, multiplication and division of the quadratic radical formula is as follows:

The order is the same as the order of Uncle Shi's operation, first multiplication and division, then multiplication and division, and finally addition and subtraction, and those with parentheses are counted in parentheses first.

In the process of arithmetic, polynomial multiplication, multiplication formulas, and arithmetic laws in rational numbers (equations) are still applicable in quadratic root operations.

In the mixed operation of addition, subtraction, multiplication and division of quadratic radicals, each radical can be regarded as a "monomial", and the sum of multiple quadratic radicals of different classes can be regarded as "polynomials".

The result of the operation is a radical, and should generally be expressed as the simplest quadratic radical.

Simplification of quadratic radicals:

First, the numerator and denominator are factorized, and the collapsed stove that can be divided is reduced, and the number of squares can be divided, or the number of squares is divided first, and then simplified through the rationalization of the denominator.

Quadratic radical hybrid operation mastery:

1. Determine the order of operations.

2. Flexible use of the law of operation.

3. Use multiplication formulas correctly.

4. Most of the denominators should be rationalized in a timely manner.

5. In some simple calculations, it may be possible to divide the points, don't be blindly rationalized.

6. Pay attention to the implicit conditions and the indication of the parentheses at the end when operating letters.

7. When mentioning the common factor, you can consider mentioning the common factor with the root number.

Quadratic radical simplification method:

The simplification of the quadratic radical form is a compulsory part of the junior high school exam, and it is often examined in the questions of junior high school competitions.

The multiplication rule of quadratic radicals: The product of the arithmetic square roots of the two factors is equal to the arithmetic square root of the products of the two factors.

Note: 1. The condition of non-negative numbers in the formula;

2. When multiplying the number of open squares, factorization should be considered.

The division rule of quadratic radicals: the quotient of the arithmetic square root of two numbers is equal to the arithmetic square root of the quotient of these two numbers.

Note: The arithmetic of multiplication and division should be used flexibly, and in the actual operation, medium-sized ants often deform from the right side of the equation to the left side of the equation, and at the same time, the value range of the letters should be considered, and finally the result of the operation should be reduced to the simplest quadratic radical.

Quadratic Argument Radical:

Addition and subtraction: only the number of squares being opened (i.e.

7 in 7) can only be added or subtracted.

Example 1（1）

Multiplication and division: Example 2

That is, multiply the number of squares to be opened).

2)2 3 posture foci 2

The result should be the simplest root (i.e., no denominator and no factor that can be broken down into integers).

Divide him and transform it into the same before you can add or subtract.

There is a certain method for learning the quadratic radical form, and if you practice it diligently, you can master it very well.

Addition and subtraction: It can be grouped into one category, and the same number under the root number can be calculated, otherwise it cannot be added or subtracted.

Multiply and divide: remember the same two root number terms when multiplying, that is, the number under the root number is the same, multiply and remove the root number; The division becomes one, and finally the denominator must be rationalized.

The most noteworthy thing to say is similar to the problem of 2 times the root number 5 plus 6 squares, at this time, it should be split in the square form of the root number A plus the root number B.

The root number term is 2 times the root number ab, and the integer term is a plus b, for example, 2 times the root number 5 is 2 times the root number 1 times times the root number 5, and 6 is 1 plus 5, so the original formula after opening the square is the root number 5 plus 1, and so on.

May you improve, and you can ask again.

(1) The addition and subtraction operation of the quadratic radical formula is similar to the addition and subtraction operation of the integer formula, and only the same kind of quadratic radical is merged.

2) Multiplication and division: a * b= ab(a 0, b 0) a b= (a b)(a 0, b 0).

3) The arithmetic laws, arithmetic rules and multiplication formulas in real number operations are still used in quadratic root operations. Note that the result of the quadratic root is the simplest quadratic radical.

(1) Knowing that x is equal to the root number 25, y is the square root of 9, find the value of 2x-5y (2) If a = root number three minus root number two, special b = root number three plus root number one-half, then which genus is larger?

4) (5 48-6 27+4 15) 3=2+4 5(5) 12 (1 2-1 12)=(12 6+12) 5(6) (root number 15 + 2 times root number 6) -39 - root number 160