Dividing Radicals and Rationalizing the Denominator - Concept

Concept Concept (1)

Long division can be used to divide a polynomial by another polynomial, in this case a binomial of lower degree. When dividing polynomials, we set up the problem the same way as any long division problem, but are careful of terms with zero coefficients. For example, in the polynomial x^3 + 3x + 1, x^2 has a coefficient of zero and needs to be included as x^3+ 0x^2+3x+1in the division problem.

Sample Sample Problems (10)

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Dividing Radicals and Rationalizing the Denominator - Problem 1

Simplify:

5√8
3x
Problem 1
How to reduce fractions with square roots.
Dividing Radicals and Rationalizing the Denominator - Problem 2

Simplify:

4
7 + √10
Problem 2
How to rationalize denominators using the conjugate.
Dividing Radicals and Rationalizing the Denominator - Problem 3

Simplify:

-3
12 + √8
Problem 3
How to rationalize denominators using the conjugate and reduce the result.
Dividing Radicals and Rationalizing the Denominator - Problem 4
Problem 4
Dividing radicals with variables and integers that are not necessarily perfect squares.
Dividing Radicals and Rationalizing the Denominator - Problem 5
Problem 5
Dividing radical monomials with integers and variables but no need to rationalize the denominator.
Dividing Radicals and Rationalizing the Denominator - Problem 6
Problem 6
Dividing radical monomials with integers and variables by simplifying each first and then rationalizing the denominator.
Dividing Radicals and Rationalizing the Denominator - Problem 7
Problem 7
Overview of rationalizing the denominator by simplifying the radical first or after the denominator has been rationalized.
Dividing Radicals and Rationalizing the Denominator - Problem 8
Problem 8
Finding the square root of fractions whether either the numerator, denominator, or both are not perfect squares.
Dividing Radicals and Rationalizing the Denominator - Problem 9
Problem 9
Dividing radical expressions with a binomial in the numerator and radical monomial in the denominator.
Dividing Radicals and Rationalizing the Denominator - Problem 10
Problem 10
Multiplying by the conjugate to divide and simplify radical expressions with a radical binomial in the denominator.