1. Complete square number

Simplify any radical with a complete square number. A complete square number is a number multiplied by itself, for example, 8 1 is 9*9. To simplify, just remove the root sign and replace it with the square root sign.

For example, 12 1 is a complete square number,11=121. You can directly remove the radical symbol and write it as 1 1. To put it simply, you should remember the complete squares of the following first twelve numbers: 1x 1 = 1, 2x2 = 4, 3x3 = 9, 4x4 = 16, 5x5 = 25, 6x6 = 36, 7x7 = 49. 9 x 9 = 8 1， 10 x 10 = 100， 1 1 x 1 1 = 12 1， 12 x 12 = 144。

2. Complete cubic number

Simplify any radical with a complete cubic number. A complete cubic number is a number obtained by multiplying a number by itself twice in a row. For example, 27 is 3*3*3. In order to simplify, just remove the root number and replace it with the cube root number. For example, 5 12 is a complete cube because 8×8×8 = 5 12. So the cube root of 5 12 is 8.

3. Radicals that cannot be completely simplified

(1) Split the root number into its own multiplier. Multiplier is a number, multiply it to get the target number. For example, 5 and 4 are a pair of multipliers of 20. We have to split the number in the radical into all possible multiplier combinations (if it is too big, try to think about it) until there is a complete square number.

For example, try to list all 45 multipliers: 1, 3, 5, 9, 15 and 45. 9 is a multiplier and a complete square number. 9 x 5 = 45 .

(2) Remove the multiplier of any complete square number. 9 is a complete square number (3*3), so put 3 out and keep 5 in the root sign. If you want to put 3 back, square it to get 9 and multiply it by 5 to get 45. 3 root number 5 is a simplified statement of root number 45.

4. Radicals with variables

(1) Find a completely flat road. What is the quadratic root of a? First,? What is the cubic root of a? A times the root sign? Answer: Because you added an exponent, A multiplied by the root number A is equivalent to the third power of A under the root number. So the complete square number here is the square of "A".

(2) Propose any variable containing a complete square number. Now take the square of a, change it to a, and put it to the left of the root sign, and get the square root of a cube, which is the root sign A.

5. Simplify radicals with numbers and variables.

(1) If there are both squares of variables in the root formula, just find the complete square number, then find the complete flattening method in the variables, and then remove the root sign to get the square root number. Let's take a look at the square root of 36 * a 2.

36 is a perfect square number, because 6×6 = 36, the square of A is a completely flat way, because it is? Square income. Now that you have turned numbers and variables into square roots, the next step is to remove the root sign and leave the square root. 36 x？ The square root of a2 is 6a.

(2) What if it is not completely flat? Let's break down the expression into two parts: numbers and variables. Find the complete square number (formula) of two parts respectively. Then put forward what can be put forward. Let's do the square root of 50*a3.

Break down 50 to find the complete square number. 25×2 = 50, and 25 is a complete square number (5×5 = 25). You can put forward 5 in the root formula, and then there are 2 left in it.

Find the complete square number in the cubic power of a, the cube of a is the square of a multiplied by a, and the square of a is a completely flat road. Put forward a and leave an a in the root symbol.

Put everything together. As long as you keep the previous proposal and the rest in the root tag as they are, and then merge (multiply) them. Five roots, two and one root, one? Merge to get 5 x? Answer? Root number 2 x a'.'