1. Definition: According to the definition of quadratic root, the square root of any non-negative number A can be expressed as √ a ... If you want to ask for a non-negative square root, you just need to write the arithmetic square root of this non-negative number.
2. Zero exponential power method: According to the nature of zero exponential power, the 0.5 power of any non-zero number is equal to the arithmetic square root of this number. We can write the number that needs to open the root sign into the form of 0.5 power of a number, and then find the arithmetic square root of this number.
3. Factorization: The square root of any positive number can be written as the product of two factors, so we can use factorization to decompose the number that needs to open the root sign into the product of several factors, and then calculate the value of the square root according to the definition of the square root.
The important role of radical sign in mathematics;
1, solving equations: the root sign can be used to solve equations, especially some quadratic equations. By factorizing or formulating the equation, the equation can be transformed into a quadratic equation with a root sign, and then the result of the root sign can be obtained, thus the solution of the equation can be obtained. For example, solving the equation x 2-6x+9 = 0 can be transformed into (x-3) 2 = 0, and then x=3 can be obtained through root operation.
2. Calculate the maximum value: the root sign can be used to calculate the maximum value. In some cases, the maximum or minimum value of a function can be obtained by root operation. For example, to find the minimum value of the function f (x) = x 2-6x-25, we can get f (x) = (x-3) 2-34 through the formula, and then get the minimum value when x=3 through the root operation.
3. Prove mathematical theorems: The root sign also plays an important role in proving mathematical theorems. In some cases, it needs to be proved by the root number. For example, when proving Pythagorean theorem, the square of Pythagorean number is equal to the sum of the squares of the other two numbers, so it needs to be proved by root sign here. The radical sign plays an important role in mathematics. It is not only a symbol, but also a mathematical concept and operation. By studying the various properties and applications of radical numbers, we can better understand and master mathematical knowledge.