What is the formula for rationalizing a denominator with a binomial?

Multiply by the conjugate of the denominator.

Rationalize the denominator: $$\frac{1}{\sqrt{2} + \sqrt{3}}$$

$$\frac{\sqrt{2} - \sqrt{3}}{-1}$$

Rationalize the denominator: $$\frac{4}{\sqrt{5} + \sqrt{2}}$$

$$\frac{4(\sqrt{5} - \sqrt{2})}{3}$$

What is the importance of rationalizing denominators in mathematics?

It simplifies expressions and makes calculations easier, especially in further operations.

Rationalize the denominator: $$\frac{9}{\sqrt{10} + 3}$$

$$\frac{9(\sqrt{10} - 3)}{-6}$$

Rationalize Denominators Flashcards

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1.

FLASHCARD QUESTION

Front

What does it mean to rationalize the denominator?

Back

Rationalizing the denominator involves eliminating any radical expressions in the denominator of a fraction, making it easier to work with.

2.

FLASHCARD QUESTION

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What is the first step in rationalizing a denominator that contains a square root?

Back

Multiply both the numerator and the denominator by the radical in the denominator.

3.

FLASHCARD QUESTION

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4.

FLASHCARD QUESTION

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5.

FLASHCARD QUESTION

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6.

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7.

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