Question

Techniques of radical and roots

Answer 1

1. Rationalizing the denominator: This technique is used to eliminate radical expressions in the denominator of a fraction. It involves multiplying both the numerator and the denominator by a conjugate of the denominator.

2. Simplifying radical expressions: This technique involves finding the perfect squares or cubes that are factors of the radicand and simplifying the radical expression.

3. Adding or subtracting radicals: This technique involves combining like terms for radicals with the same index (square root, cube root, etc.) and adding or subtracting their coefficients.

4. Multiplying and dividing radicals: This technique involves simplifying the product or quotient of two radical expressions by using the product or quotient rules of radicals.

5. Rational exponents: This technique involves converting radical expressions to expressions with rational exponents and simplifying them using the rules of exponents.

6. Completing the square: This technique is used to solve quadratic equations by adding and subtracting a constant to both sides of the equation to create a perfect square trinomial, which can then be factored.

7. Solving cubic equations by factoring: This technique involves factoring the cubic equation into linear and quadratic factors which can be solved using techniques such as completing the square or factoring by grouping.

8. Solving higher degree equations: Techniques such as synthetic division, polynomial long division, and factoring by grouping can be used to solve equations of higher degrees.