# Rationalizing a denominator quotient involving higher radicals and monomials

- Simplify radical expressions
- Radicals: Rationalizing the Denominator
- Intro to rationalizing the denominator
- Rationalize radical denominator

## Simplify radical expressions

Multiplying a univariate polynomial by a monomial with a positive coefficie .. Rationalizing a denominator - Quotient involving higher radicals and monomials .

and your and forThis calculator eliminate a radicals in a denominator. It can rationalize radical denominators with 2 radicals or less. Replace radical sign with letter r. Welcome to MathPortal. I designed this web site and wrote all the lessons, formulas and calculators. If you want to contact me, probably have some question write me using the contact form or email me on.

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Simplifying square-root expressions: no variables. Simplifying square roots of fractions. Simplifying rational exponent expressions: mixed exponents and radicals. Simplifying square-root expressions: no variables advanced.

On the previous page, all the fractions containing radicals or radicals containing fractions had denominators that cancelled off or else simplified to whole numbers. What if we get an expression where the denominator insists on staying messy? This looks very similar to the previous exercise, but this is the "wrong" answer.

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That's a mathematical symbols way of saying that when the index is even there can be no negative number in the radicand, but when the index is odd, there can be. The radicand contains no factor other than 1 which is the n th or greater power of an integer or polynomial. An expression with a radical in its denominator should be simplified into one without a radical in its denominator. This process is called rationalizing the denominator. This is accomplished by multiplying the expression by a fraction having the value 1, in an appropriate form. To rationalize this denominator, the appropriate fraction with the value 1 is , since that will eliminate the radical in the denominator, when used as follows:. What can be multiplied with so the result will not involve a radical?

## Radicals: Rationalizing the Denominator

ALGEBRA: Rationalizing The Denominator

## Intro to rationalizing the denominator

If we combine these two things then we get the product property of radicals and the quotient property of radicals. These two properties tell us that the square root of a product equals the product of the square roots of the factors. The answer can't be negative and x and y can't be negative since we then wouldn't get a real answer. In the same way we know that. These properties can be used to simplify radical expressions.

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## Rationalize radical denominator

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