Simplification of the root number, how to simplify the root number

The root number simplification method is to split the number under the root number into a perfect square number and the product of a certain number, and then put the perfect square number outside the root number, but only if the number inside the root number is an integer, if it is a fraction, then the fraction is split into the square number of a fraction and the product of a certain number.

The root sign is a mathematical symbol, and it is also used to represent the symbol of the opening operation of a number or an algebraic formula, if a = b, then a is the nth power root of b to the nth power or a is the 1 n power of b, the handwriting and printing font of the open n power are represented, and the number or algebraic formula of the square is written on the right side of the left side of the symbol and the lower part of the horizontal part above the symbol in the area that is enclosed together, and cannot go out of bounds. If the number is even, divide by 2.

If the number is even, then the first thing you can do is divide by 2. In this example, 98 becomes (2x49) because 98 divided by 2 is 49. If your number is not divisible by 2, try 3, 4, 5, and so on until you get a factor.

Formula: root number (a b) = (root number a) (root number b).

Root number 8 = root number (4 2) = (root number 4) (root number 2) = 2 root number 2 = 2 root number 2

8 = 2 * 4, 4 is a perfect square number, is 2 squared, so it can be opened from the root number, if a number has a factor is a complete square number, you can continue to open the root number simplified.

You can multiply the square of the 2 outside the root number by the 2 in the root number

That is, 8 is to break down 8 into 2 times 4

Make 4 2

So it's 2 root number 2

**What is the rule, it is ordinary simplification.

Root number 8 = 2 * 4 under root number = 2 * 2 squared under root number.

Isn't the square of 2 just 2 times the root number 2?

Start by writing a number as the product of several square numbers.

The square number can be opened.

The root numbers 1 to 100 are simplified as follows:

<> Root number writing specification:

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.

N to the nth power is written on the left side of the symbol, and n can be ignored when n=2 (square root), but it must be written if it is a cubic root (cubic root), a fourth square root, etc.

There are two ways to reduce a quadratic radical to the simplest quadratic radical:

1. If the square number is an integer or an integer, first decompose it into a factor or factor, and then remove the root number from the perfect square or square number to simplify the radical.

2. If the number of the opened square is a fraction or fraction (including decimals), the denominator is rationalized first, and then simplified according to the situation that the opened square is an integer or an integer.

It can be seen that there are two essentials of simplifying the quadratic radical: one is that the denominator is rationalized; The second is to decompose the factor (factor) and open the perfect flat method (number) out of the root number.

The simplest radical is an important concept of the radical, in the process of the radical operation, from beginning to end through the simplification of the radical, students should learn the method of simplifying the radical, the steps of the simplification of the quadratic radical can be briefly summarized as "open", "complement" two words.

The first step is "open", that is, in the factors of the open mode, they can be replaced by their arithmetic square roots, and those that can be moved outside the root number are moved to the outside of the root number, so that the exponent of each factor of the new open mode is less than the root index 2;

The second step is to "complement", that is, to multiply the denominator and the numerator of the new opening method by the denominator itself, so that after the denominator is multiplied by itself, the new denominator can all be opened outside the root number, so as to achieve the purpose of the opening method without the denominator.

Problem 1: How to simplify the root number 4=2 8=2 2 2 9=3 12=2 3

Problem 2: How to simplify the root number fraction Simplify the root number fraction: that is, the denominator is rationalized, there are many methods, the first is to use the square difference formula to simplify the root number in the denominator.

The second is to multiply the numerator and denominator by the denominator at the same time to remove the root number of the denominator. The third type: multiple root numbers need to be radicalized into fractional exponential powers, using the operational properties of powers.

For example: 8/2 Simplify:

Quadratic radical simplification process:

Turning fractions or decimals into false fractions;

decompose the open square number into prime factors or factorization;

Move the factors or factors that can be opened to the end of the root sign outside the root number;

remove the denominator from the root number, or remove the root number from the denominator;

Approximation. <>

The root number is a mathematical symbol. The root sign is a symbol used to represent the opening operation of a number or an algebraic formula. If a = b, then a is the nth root of b to the nth power or a is the 1 nth power of b.

The formula for calculating the root number:

Condition: a 0, n 2 and n n.

Condition: a 0, b 0, n 2 and n n.

Condition: a 0, b 0, n 2 and n n.

Condition: a 0, b 0, n 2 and n n.

The inside of the root number becomes perfectly squared, and then squared.

For example: root number (3+2 root number 2).

Root number [1+2 root number 2+2].

Root number [1 square + 2 root number 2 + (root number 2) square].

Root number [(1 + root number 2) square].

1 + root number 2

The root number is simplified as follows:

Definition of root number:

The root number is a mathematical symbol. A root sign is a symbol used to represent an open square operation on a number or a sharp algebraic formula. If a = b, then a is the nth root of b to the nth power or a is the 1 nth power of b.

The open n power handwriting and printing font are represented by n, and the number or algebraic writing late base book is in the area enclosed by the right side of the symbol to the left and below the code macro of the horizontal part above the symbol, and cannot go out of bounds. <>