What is the operation of addition and subtraction of root numbers? Formula?

The numbers in the root number can be made identical, or the same can be added or subtracted, and different numbers cannot be added or subtracted.

If the numbers in the root number are the same, you can add or subtract, if the numbers in the root number are not the same, you can't add or subtract, and if you can reduce it to the same number in the root number, you can add or subtract.

For example: 1) 2 2 +3 2=5 2 (the numbers in the root number are all 2 and can be added).

2) 2 3 +3 2 (one number in the root number is 3, one is 2, and the difference cannot be added).

3) 5 + 20 = 5 + 2 5 = 3 5 (although the numbers in the root number are different, they can be made into the same and can be added).

First simplify the radical, if the numbers under the root number are different after simplification, they cannot be added or subtracted, if the numbers under the root number are the same after simplification, they can be added or subtracted, the numbers in the root number remain unchanged, and the numbers outside are added and subtracted. For example, 2x root number 21 plus 6x root number 21 equals 8x root number 21.

Subtraction is the same thing, and the root number is never the same. Multiplication and division of the root formula is different from addition and subtraction, but it should also be simplified first, and the numbers under the two root numbers are multiplied and divided after subtraction, and the numbers outside the two root numbers are divided by each other.

How to calculate addition, subtraction, multiplication and division of the root number.

1 square root shorthand formula table.

Negative roots don't work, and zero takes the square root and it remains zero. There are two positive square roots, and the sign opposite values are the same. 2. The root finger can be omitted, and the others must be indicated. Negative numbers have only odd roots, and the arithmetic square root is zero or positive.

a×√b=√a×b

a/√b=√a/b

The addition and subtraction of the root number needs to be replaced with the same kind of term, which is calculated by the multiplicative distributive property.

For example: 24+ 54=2 6+3 6= 6(2+3)=5 6 The same goes for subtraction.

Hope it helps.

In the operation of the addition and subtraction of the root number, first the number in the root number will be opened if it can be opened, and the number in the root number is the same, and then the coefficients in front of them will be added and subtracted, and the number obtained will be used as the new coefficient. If the root number is different, it can no longer be calculated.

There can be formulas for this, and specific problems can be solved.

Quadratic Radical:

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

7 of 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).

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

What can be added is added, and what can't be simplified with compound quadratic radical (square (a+b) 2, (a-b) 2 in the root number, open the square first if it can't match, and then open the root number after the operation is the simplest). For example:

a^2+2ab+b^2=a+b

The rules for addition, subtraction, multiplication, and division of root numbers are as follows:

1.Addition and subtraction of root numbers:

The addition and subtraction of the root number of two numbers must be the same kind under the same root number, that is, the number in the root number is the same, in order to add or subtract the operation.

For similar terms under the same root number, you can add or subtract the numbers inside the root number, and the coefficient outside the root number remains unchanged, that is, $ sqrt pm sqrt = 2 sqrt$.

Items under different root numbers cannot be added or subtracted.

For example, $ sqrt+ sqrt=2 sqrt$, but $ sqrt+ sqrt$ cannot be added or subtracted.

2.Pitan multiplication of root numbers:

The root number can be thought of as a power of the exponent $ frac$, so multiplying the two root numbers is equivalent to the addition of the exponents, i.e. $ sqrt times sqrt = sqrt$.

For example, $ sqrt times sqrt= sqrt$.

3.Division of the root number:

The root number can be seen as a power of the exponent $ frac$, so the division of the two root numbers is equivalent to the subtraction of the exponent, i.e. $ frac}} sqrt}$。

For example, $frac}} =sqrt}= sqrt=2$。

It should be noted that the operation priority of the root number touching the chain is different from the general operation symbol priority, so when performing complex root number operation, it is necessary to add parentheses according to the specific situation to ensure the correctness of the operation.

The root number addition, subtraction, multiplication and division algorithm is a+ b= b+ a, a- b=-(b- a), a b= (ab), a b= (a b), etc.

Addition and subtraction of the first and second radicals.

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

Note: 1. The addition and subtraction of the quadratic radical formula is usually divided into two steps, the first step is simplified, and the second step is merged.

2. Before merging, it should be noted that it is necessary to determine which of the quadratic radicals in them have the same number of open squares; When merging, it is similar to the previous merge of similar terms, only the factor outside the root number needs to be added or subtracted, and the number of squares and the root exponent remain unchanged.

2. Multiplication and division of quadratic radicals.

Quadratic radical multiplication, etc., is disturbed by the arithmetic square root of the product of the square number being opened.

The division of quadratic radicals is equal to the arithmetic square root of the quotient of the square number to be opened.

Writing conventions for root numbers:

1. Write the root number:

First draw a short diagonal line to the upper right corner in the middle of the grid, and then continue to draw the lower right middle diagonal line with the strokes, and then draw a horizontal line of moderate length according to the needs of the finch near the top of the grid, and then make up for it if it is not enough.

2. Write the number or formula of the square to be opened:

The number or algebraic formula to be opened is written in the area enclosed by the right side of the V-shaped part on the left side of the symbol and the lower part of the horizontal part above the symbol, and cannot go out of bounds, if the number or algebraic formula of the square is too long, the upper horizontal must be extended to ensure that the open square or algebraic formula below is covered.

3. Write the square number or formula:

n to the nth power is written on the left side of the symbol, n=.

The radical addition and subtraction rule is one of the operation rules of the radical, several radicals are added and subtracted, each radical is first reduced to the simplest radical, and then the same radical is merged, and the radicals of different classes are written together with operator symbols.

Expand the scum stupid exhibition information:

The addition and subtraction of radicals is the law of addition and subtraction of each radical, and the radical should be reduced to the simplest radical first, and then the remainder or the same radical should be combined.

The rule of addition and subtraction of quadratic radicals first simplifies each quadratic radical into the simplest quadratic radical, and then merges the same quadratic radicals separately.

Homogeneous radicals, also known as similar radicals, is an algebraic term that refers to the radicals that are allowed to be combined when doing addition and subtraction.