Rationalizing the Denominator (1st)

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.

Front

What is the result of rationalizing the denominator of the fraction 1/√2?

Back

The result is √2/2.

Front

How do you rationalize the denominator of a fraction with a binomial denominator, such as 1/(a + b)?

Back

Multiply the numerator and denominator by the conjugate of the denominator, which is (a - b).

Front

What is the conjugate of the expression (3 + √5)?

Back

The conjugate is (3 - √5).

Front

If you have the expression 5/√3, what is the first step to rationalize the denominator?

Back

Multiply both the numerator and denominator by √3.

Front

What is the simplified form of 10/√5 after rationalizing the denominator?

Back

The simplified form is 2√5.

Front

Why is it important to rationalize the denominator in mathematical expressions?

Back

Rationalizing the denominator can simplify calculations and make expressions easier to understand.

Front

What is the general formula for rationalizing a denominator of the form 1/√x?

Back

Multiply by √x/√x to get √x/x.

Front

How do you rationalize the denominator of a fraction like 4/(2 + √3)?

Back

Multiply the numerator and denominator by the conjugate (2 - √3).

Front

What is the result of rationalizing the denominator of 7/(√2 + 1)?

Back

The result is (7(√2 - 1))/1 = 7√2 - 7.