What is a root number? How to prescribe? How to prescribe the root number?

Root number The positive nth root of the positive number a, denoted by the symbol "". The symbol "" is pronounced as "nth root number", abbreviated as "".

At first, around 1480, the Germans used a dot (·) to represent the square root, such as. 3 is 3 with square roots, ·· Indicates the 4th power root, ·· denotes the cube root. By the beginning of the 16th century, a small dot with a tail became " " " probably when writing fast.

In 1525, the German mathematician Rudolph's algebra book was noted.

Later, in his Geometry, Descartes first created the modern square root symbol "". In the first edition of the original book it was written:

If I want to find the square root of a2+b2, I write, and if I want to find the square root of a2-b2+abc, I write".

There are two differences between the root number of Descartes and the root number of Rudolph. Descartes considered that Rudolph's root number would be confusing when there were several terms in the number of squares to be opened. Therefore, he connected the terms with brackets at the top, and put a mark in front of them".

In addition, Descartes' root number has a small hook more than Rudolph's root number.

The current cube root symbol appeared much later, and it was not seen in some books until the 18th century. It was not until 1732 that it became popular. Later, the general n-power root symbol will also appear.

The power root of n (n is a natural number) of the number a refers to the number where the power of n is equal to a, that is, the number b suitable for bn a. For example, the 4th power root of 16 has 2 and 2. The 2nd power root of a number is called the square root; The 3rd power root is called the cube root.

The power roots are collectively referred to as square roots. The operation of finding the square root of a given number is called an open square. The question of how many square roots there are in a number is related to both the range of the number and the number of square roots.

In the range of real numbers, there is only one odd root of any real number, e.g. the 3rd root of 8 is 2, and the 3rd root of 8 is 2; The even square root of a positive real number is two numbers that are opposite to each other, e.g. the 4th power root of 16 is 2 and 2;There is no even root for negative real numbers; Any power root of zero is zero. In the range of complex numbers, whether n is odd or even, any non-zero complex number has n roots to the nth power. If the complex number z r (cos i sin), r z , then its n n roots are , k 0, 1, 2....，n－1。

Open square Multiply the same two numbers.

Prescription method: 1. For example, if we calculate the root number 10, partners with computers can press it, and the result will be before and after the decimal point, and every two digits will be divided. Then you can make up 0 before and after.

2. Then start from the leftmost section, because it is a section every two digits, so the leftmost number must be less than equal.

99, so find a number within 10 that is the largest and less than the first section, as the first number of the square. So the first value you get from 10 square is 3

3. Just like doing division, 10 minus 3 squared is 9, the remainder.

It's 1, and then move the number of the second stanza down, and we're making up 00 here, so it's 100.

4. Then calculate the second number, first use 20 to multiply by 3, that is, the first one to get x, you can get a number, you can mark it as y, in our case y is 60, and then use the remainder of the previous step to remove this y, which is 60. In short, it is 100 divided by 60, and the integer bit is the value of the second number, so it is 1.

5. Then add 1 to 60 in step 5, multiply by 1, 1 * (60 + 1) is equal to 61, and then use the remainder 100 to subtract 6, and then move the number of the second section down, here is also 00Then subtract and we can get the remainder of 3900, and then repeat the above steps 5 and 6 in turn to get an infinite approximate result.

Put the formula in the root number and match it with a completely flat method, and you can open the square.

For example, the formula in the root number is: 3+2 2, then.

Re-open the square to get 2+1

Of course, just write the equal sign " " in the process, and I don't need to write a lot like this.

If the root number is three, four, and so on.

Root number 2 is approximately equal to, root number 3 is approximately equal to, root number 5 is approximately equal to, root number 7 is approximately equal to.

Radical multiplication and division rule:

1. Multiply (divide) by the same radical, multiply (divide) the coefficients in front of the radical as the coefficient of the product (quotient); Multiply (divide) the open square number as the opened square number, the root exponent does not change, and then it is reduced to the simplest radical formula.

2. Multiplication (division) of non-same radicals should be first transformed into the same radical, and then the spine wheel should be calculated according to the rule of multiplication (division) of the same radical.

The law of addition and subtraction of radicals instructs: to add and subtract each radical, Sakura Shin should first turn the radical into the simplest radical, and then merge the same radical. Quadratic radical addition and subtraction rule: First, reduce each quadratic radical to the simplest quadratic radical.

Then put the same kind of quadratic radical.

Merge separately. In the addition and subtraction of radicals, homogeneous radicals are combined. In general, several radicals can always be formed into the same radical, but not necessarily into the same radical.

Sum of square rootsArithmetic square rootThe difference:

1. The definition is different: if x2=a, then x is called the square root of a. A positive number has two square roots, and they are opposites of each other; There is a square root, which is 0 itself; Negative numbers do not have square roots; If x2=a, and x 0, then x is called the arithmetic square root of a, and there is only one arithmetic square root of a positive number, and the arithmetic square root of a non-negative number must be a non-negative number.

2. Different representations: the square root of a positive number a, expressed as a; The arithmetic square root of a positive number a is a.

1.Method of opening the root number: factorization. Swap the number for the product of the square and the number.

2.For example: 12=2 2 3=2 squared 3 , 12= (2 squared) 3=2 3;

8=2 2 2=2 squared 2, 8= (2 squared) 2=2 2;

6 = 2 3, there is no square, so you can't open the root number;

18=3 3 2=3 squared 2, 18= (3 squared) 2=3 2.

The square is the inverse of the square. Such as the square of a b. Huai Jing.

Then the square root number of b is A.

The root number is a symbol used by Lead Liang Shen to represent the opening operation of a number or an algebraic formula.

If a n=b, then a is the nth root of b to the nth power or a is the 1 nth power of b.

Open nth power handwriting and printing are denoted by .

Root Number Introduction:The root number is a mathematical slag 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 n power of b.

The open nth power handwriting and typography are denoted by the number or algebraic form written on the left side of the symbol and the area below the horizontal part above the symbol, and cannot go out of bounds.