Rationalizing Denominators

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

Front

Why is it important to rationalize the denominator?

Back

Rationalizing the denominator simplifies expressions and makes them easier to work with, especially in further calculations.

Tags

CCSS.HSN.RN.A.2

Front

What is the general method for rationalizing a denominator that contains a square root?

Back

Multiply the numerator and denominator by the square root in the denominator.

Front

Rationalize the denominator: 1/√2

Back

(1/√2) * (√2/√2) = √2/2.

Front

Rationalize the denominator: 3/(2+√3)

Back

Multiply by (2-√3)/(2-√3) to get (3(2-√3))/(4-3) = 3(2-√3)/1 = 6-3√3.

Tags

CCSS.HSN.RN.A.2

Front

What is the result of rationalizing the denominator of 5/(√5)?

Back

(5/(√5)) * (√5/√5) = 5√5/5 = √5.

Tags

CCSS.HSN.RN.A.2

Front

Rationalize the denominator: 4/(√7 - 1)

Back

Multiply by (√7 + 1)/(√7 + 1) to get (4(√7 + 1))/(7 - 1) = (4√7 + 4)/6 = (2√7 + 2)/3.

Tags

CCSS.HSN.RN.A.2

Front

What happens to the value of a fraction when you rationalize the denominator?

Back

The value of the fraction remains the same; only the form of the expression changes.

Front

Rationalize the denominator: 1/(√x + 2)

Back

Multiply by (√x - 2)/(√x - 2) to get (√x - 2)/(x - 4).

Tags

CCSS.HSN.RN.A.2

Front

What is the conjugate of a binomial expression like (a + b)?

Back

The conjugate is (a - b). It is used to rationalize denominators.

Tags

CCSS.HSN.CN.A.3