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 expression 10/√5?

Back

The result is 2√5.

Front

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

Back

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

Front

If you have the expression 1/√a, how would you rationalize it?

Back

Multiply both the numerator and denominator by √a to get √a/a.

Front

What is the simplified form of 3/√2 after rationalizing the denominator?

Back

The simplified form is (3√2)/2.

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 result of rationalizing the denominator of 5/(2√3)?

Back

The result is (5√3)/6.

Front

How do you rationalize a denominator with a binomial expression, such as 1/(a + √b)?

Back

Multiply the numerator and denominator by the conjugate (a - √b) to eliminate the square root.

Front

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

Back

The conjugate is (a - √b).

Front

What happens to the denominator when you multiply by the conjugate?

Back

The denominator becomes a difference of squares, eliminating the square root.