1, one of the basic methods of rationalization is the rational denominator.
For a fraction with a root sign, we can eliminate the root sign in the denominator by multiplying it by an appropriate factor. For example, if we have a score of1√2, we can take the denominator as √ 2, that is, multiply it by √2/√2 to get √2/2. In this way, we have transformed an irrational number into a rational number.
2. Another method of rationalization is to eliminate the root sign by squaring.
If we have a formula with a square root, we can square it and get a rational number without a root sign. For example, if we have a formula √3, we can square it to get 3. In this way, we have transformed an irrational number into a rational number.
3. Some special radical formulas can be rationalized by some mathematical formulas.
For example, a formula with two root signs can be rationalized by quadratic variance formula. The formula is (x+y) (x-y) = x 2-y 2, where x and y respectively represent the numbers in the two radicals. Through this formula, we can transform a formula with two root signs into a rational number without root signs.
Matters needing attention in radical systematization and handling complex situations;
1. Precautions for radical rationalization
Formulas with roots can be transformed into rational numbers by physical and chemical methods. These methods include rationalization of denominator, elimination of root sign by square, rationalization by mathematical formula and approximation. However, not all radical formulas can be rationalized, because some radical formulas represent irrational numbers. In these cases, we can only use approximate values to calculate.
Some radical formulas cannot be rationalized because they represent irrational numbers and cannot be expressed as finite decimals or fractions. In this case, we can only express these equations by approximation.
2. Handling of complex situations
In some complicated cases, mathematical approximation can be used to rationalize. For example, Taylor series expansion can be used to approximate formulas with root signs. An approximate rational number can be obtained by intercepting the finite term of the series.