First, the multiplication rule of radical sign
This algorithm is one of the most basic rules in radical operation. When a and b are both square numbers, the product is simplified to the product of two root numbers. √ (a * b) = √ a * √ B. This rule is very useful in solving complex mathematical problems because it simplifies the operation under the root sign.
Second, the division rules of the root number
The algorithm is similar to multiplication but involves division. According to this rule, √ (a/b) = √ a/√ B. In the division operation under the root sign, both the dividend and the divisor are squares, and then the division is converted into multiplication.
Third, the fundamental symbol of the law of power operation
This algorithm allows to simplify the power under the root sign. According to this law, √ (a n) = (a n) (1/n), where n is a positive integer. The application of this rule greatly simplifies the complex expressions under the root sign.
Fourthly, the exponential algorithm of root number.
The algorithm includes the combination of root sign and exponent. According to this law, (√ a) n = √ (a n), where n is a positive even number. This rule is very useful in dealing with the mixed operation of root sign and exponent, which transforms the exponential operation into the operation under root sign, thus simplifying the problem.
Practical application of root sign
I. Measurement and calculation
In the field of architecture and engineering, when determining the size or length of an object, it is necessary to use measuring tools, such as rulers and tape measures. In some cases, the length of an object cannot be measured directly, and it needs to be calculated by trigonometric function or Pythagorean theorem, and the root sign symbol will be used in these calculations.
Second, solve geometric problems.
Given the side length of a square, find the area of the square and solve it with the root sign. Calculate the square of the side length, take out the side length with the root sign, and finally multiply it by a real number to get the area. Another application is to find the area of a circle. As long as the radius of the circle is brought into the root form and the result is multiplied by the area of the circle, the area of the circle can be found.