Rationalizing Denominators: How to Remove Roots from the Bottom of Fractions

The video tutorial explains the process of rationalizing denominators, which involves removing roots from the bottom of fractions to make them rational. It covers the reasons for this practice, including historical context and practical benefits. The tutorial provides step-by-step instructions for rationalizing simple square roots and more complex denominators using conjugates. The importance of practice is emphasized to master the topic.

What is the main goal of rationalizing a denominator?

• To make the numerator a whole number

• To convert the fraction into a decimal

• To remove roots from the denominator

• To simplify the fraction to its lowest terms

Why was rationalizing denominators important before calculators?

• It was a method to check for errors

• It made manual calculations easier

• It helped in converting fractions to decimals

• It was required by mathematical laws

When rationalizing a denominator with a single square root, what should you multiply by?

• The reciprocal of the fraction

• The square root itself

• The square of the root

• The numerator of the fraction

What is the result of multiplying √2 by itself?

• √2

• 1

• √4

• 2

What is the conjugate of 3 + √2?

• 3 + √2

• 3 - √2

• √2 - 3

• 2√3

What happens to the terms involving roots when multiplying by the conjugate?

• They double

• They cancel out

• They become negative

• They remain unchanged

What is the simplified form of 5/(3 + √2) after rationalizing the denominator?

• 5√2/3

• (5√2 - 15)/7

• (15 - 5√2)/7

• 5/(3 - √2)