Rationalizing Radicals and Fractions

This video tutorial explains how to rationalize the denominator of a fraction by multiplying both the numerator and denominator by a radical that will eliminate the radical in the denominator. Two examples are provided: one with the fraction 1 over the square root of 14 and another with 6 over the square root of 6. The tutorial demonstrates the process of multiplying by the appropriate radical to achieve a rational denominator and emphasizes the importance of simplifying the resulting fraction.

What is the primary goal of rationalizing the denominator?

• To convert the fraction into a decimal

• To simplify the numerator

• To eliminate the radical from the denominator

• To make the numerator a perfect square

In the first example, why does the square root of 14 not simplify?

• Because 14 is an even number

• Because 14 is a prime number

• Because 14 has no perfect square factors

• Because 14 is a composite number

What do you multiply the numerator and denominator by to rationalize 1/√14?

• 14

• 1/√14

• √14

• 2√7

After rationalizing 1/√14, what is the resulting expression?

• √14/14

• 1/14

• 14/√14

• 1/√14

What is the first step in rationalizing 6/√6?

• Divide by √6

• Divide by 6

• Multiply by √6

• Multiply by 6

Why does the square root of 6 not simplify?

• Because 6 is a prime number

• Because 6 has no perfect square factors

• Because 6 is an even number

• Because 6 is a composite number

What is the result of multiplying the numerator and denominator by √6 in the second example?

• 6/6

• 6√6/6

• 6/√6

• √6/6

After rationalizing and simplifying 6/√6, what is the final expression?

• 6√6

• 6

• √6

• 1

What should you always check for after rationalizing a denominator?

• If the fraction can be simplified further

• If the numerator is a perfect square

• If the fraction is a whole number

• If the denominator is a prime number

What is the rational form of the square root of 6 as a fraction?

• √6/1

• 6/1

• 1/√6

• √6/6