What is the conjugate of the expression $$a + b\text{√}c$$ ?

The conjugate is $$a - b\text{√}c$$ .

How do you rationalize the denominator of $$\frac{1}{\sqrt{7}}$$ ?

Multiply the numerator and denominator by $$\sqrt{7}$$ to get $$\frac{\sqrt{7}}{7}$$ .

What is the conjugate of $$6 - 3\sqrt{2}$$ ?

The conjugate is $$6 + 3\sqrt{2}$$ .

Multiply: $$(4 + \sqrt{2})(4 - \sqrt{2})$$

The result is $$16 - 2 = 14$$ .

What is the conjugate of the expression $$2 + 3\sqrt{7}$$ ?

The conjugate is $$2 - 3\sqrt{7}$$ .

What is the first step in rationalizing a denominator with a binomial?

Multiply by the conjugate of the denominator.

If you have $$\frac{1}{\sqrt{a} + \sqrt{b}}$$ , how do you rationalize it?

Multiply by $$\frac{\sqrt{a} - \sqrt{b}}{\sqrt{a} - \sqrt{b}}$$ .

What is the result of $$\frac{1}{\sqrt{3}}$$ after rationalizing?

The result is $$\frac{\sqrt{3}}{3}$$ .

What is the purpose of rationalizing the denominator?

To simplify the expression and make it easier to work with.

What is the result of $$\frac{5}{\sqrt{5}}$$ after rationalizing?

The result is $$\frac{5\sqrt{5}}{5} = \sqrt{5}$$ .

How do you rationalize $$\frac{1}{\sqrt{2} + 1}$$ ?

Multiply by $$\frac{\sqrt{2} - 1}{\sqrt{2} - 1}$$ .

What is the result of $$\frac{1}{\sqrt{10}}$$ after rationalizing?

The result is $$\frac{\sqrt{10}}{10}$$ .

What is the general formula for rationalizing a denominator of the form $$\sqrt{a} + \sqrt{b}$$ ?

Multiply by the conjugate $$\sqrt{a} - \sqrt{b}$$ .

Dec 2 Rationalize the Denominator

Flashcard

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Mathematics

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9th - 12th Grade

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Practice Problem

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Hard

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CCSS

HSN.RN.A.2, HSN.CN.A.3, 7.NS.A.2C

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FLASHCARD QUESTION

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What does it mean to rationalize the denominator?

Back

Rationalizing the denominator means to eliminate any irrational numbers (like square roots) from the denominator of a fraction.

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CCSS.HSN.RN.A.2

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CCSS.HSN.CN.A.3

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FLASHCARD QUESTION

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FLASHCARD QUESTION

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CCSS.HSN.CN.A.3

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CCSS.HSN.RN.A.2

FLASHCARD QUESTION

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CCSS.HSN.CN.A.3

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