What is the formula for rationalizing a denominator of the form $$a + b$$ ?

Multiply by the conjugate: $$\frac{1}{a + b} \cdot \frac{a - b}{a - b}$$ .

Rationalize the denominator: $$\frac{4}{\sqrt{7} + 3}$$

Multiply by the conjugate: $$\frac{4(\sqrt{7} - 3)}{7 - 9} = -2(\sqrt{7} - 3)$$ .

Rationalize the denominator: $$\frac{2}{\sqrt{8} - 2}$$

Multiply by the conjugate: $$\frac{2(\sqrt{8} + 2)}{4} = \frac{\sqrt{8} + 2}{2}$$ .

What is the importance of rationalizing the denominator in mathematics?

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

Resource Library

Math

Algebra

Rationalizing The Denominator

Rationalizing Denominators

Flashcard

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSN.RN.A.2, HSN.CN.A.3

Standards-aligned

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15 questions

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FLASHCARD QUESTION

Front

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.

Tags

CCSS.HSN.RN.A.2

FLASHCARD QUESTION

Front

What is the process to rationalize the denominator of $\frac{a}{\sqrt{b}}$ ?

Back

Multiply both the numerator and the denominator by $\sqrt{b}$ to get $\frac{a\sqrt{b}}{b}$ .

Tags

CCSS.HSN.RN.A.2

FLASHCARD QUESTION

Front

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

Back

$\frac{\sqrt{2}}{2}$ .

FLASHCARD QUESTION

Front

Rationalize the denominator: $\frac{3}{\sqrt{5}}$

Back

$\frac{3\sqrt{5}}{5}$ .

FLASHCARD QUESTION

Front

Rationalize the denominator: $\frac{\sqrt{7}}{\sqrt{3}}$

Back

$\frac{\sqrt{21}}{3}$ .

Tags

CCSS.HSN.RN.A.2

FLASHCARD QUESTION

Front

What is the result of rationalizing $\frac{\sqrt{8}}{\sqrt{2}}$ ?

Back

$\frac{4}{2} = 2$ .

Tags

CCSS.HSN.RN.A.2

FLASHCARD QUESTION

Front

Rationalize the denominator: $\frac{5}{\sqrt{6}}$

Back

$\frac{5\sqrt{6}}{6}$ .

Tags

CCSS.HSN.RN.A.2

FLASHCARD QUESTION

Front

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

Back

Multiply by the conjugate: $\frac{2(\sqrt{3} - 1)}{2} = \sqrt{3} - 1$ .

Tags

CCSS.HSN.RN.A.2

FLASHCARD QUESTION

Front

What is the conjugate of $\sqrt{3} + 1$ ?

Back

The conjugate is $\sqrt{3} - 1$ .

Tags

CCSS.HSN.CN.A.3

10.

FLASHCARD QUESTION

Front

Rationalize the denominator: $\frac{1}{\sqrt{5} - 2}$

Back

Multiply by the conjugate: $\frac{\sqrt{5} + 2}{1} = \sqrt{5} + 2$ .

Tags

CCSS.HSN.RN.A.2

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