Radical operation is one of the most basic surgical methods. The arithmetic roots are opened to the nth power, the root index is expanded to n times, and the number of roots remains the same. Non-arithmetic roots are not always possible. When the odd root of a negative number is transformed into an odd power, the given root is generally transformed into an arithmetic root, and then the root is found according to the law.
1. Multiply the root number 2 by 2, then multiply 2 by the root number 4, that is, multiply the root number 4 by the product of the root number 2, and then multiply the number 2 under the root number by the number 4 of zhi4, that is, the root number 8, which can also be simplified to twice the root number 2.
For example: √ Road 2 * 2 = 2 √ 2 * √ 4 = √ (2 * 4) = √ (2 2 * 4) = √ 8.
2. The square root of the root number 3 times 6 is the product of 6 times 3 under the root number, that is, the root number 18, and then the root number 18 becomes 9 times 2, because 9 can root, so the root number 2 is 3 times.
For example: √ 3 *√ 6 = √ (3 * 6) = √18 = √ (9 * 2) = √ 32 * 2) = 3 √ 2.
3. Multiply the root number 32 by the root number 25 to get the root number 800. The root number 800 drops to the product of 400 times 2 at the root number, and 400 is equal to 20 times 20, which is the square of 20. Finally, the root number 2 was reduced to 20 times.
For example: √ 32 * √ 25 = √ (32 * 25) = √ 800 = √ (400 * 2) = √ (202 * 2) = 20 √ 2.
Root-type high-frequency test sites ① simplify the secondary roots according to the range of letters;
② Determine the range of letters according to the simplification result of quadratic root;
③ Using the property of quadratic roots to find the minimum (maximum) value of letters (or algebraic expressions);
(4) using the square difference formula to calculate the evaluation denominator; In addition, it is an investigation of the simplest quadratic root, similar quadratic root and other related basic knowledge.
The radical attribute is in the real number range:
(1) Even root number cannot be negative, and its operation result is not negative.
(2) It can be negative under odd root sign.
Not limited to real numbers, that is, when considering imaginary numbers, even roots can be negative numbers, and i=√- 1 can be used.
The above is some information about the roots of mathematics, hoping to help everyone.