Rationalizing Fractions and Square Roots

The video tutorial explains how to rationalize the denominator of fractions by multiplying both the numerator and denominator by a radical that will eliminate the radical in the denominator. Two examples are provided: rationalizing 20 over the square root of 10 and 35 over 3 times the square root of 7. The process involves identifying the irrational denominator, multiplying by the appropriate radical, and simplifying the resulting fraction. The importance of simplifying the fraction to its simplest form is emphasized.

What is the purpose of rationalizing the denominator?

• To convert the fraction into a decimal

• To eliminate the radical from the denominator

• To simplify the numerator

• To make the numerator a whole number

In the first example, what is the initial fraction given?

• Square root of 10 over 20

• 20 over 10

• 20 over the square root of 10

• 10 over the square root of 20

What do you multiply the numerator and denominator by to rationalize 20 over √10?

• Square root of 5

• Square root of 10

• Square root of 20

• 10

What is the result of multiplying the square root of 10 by itself?

• 10

• 20

• Square root of 100

• Square root of 20

After rationalizing 20 over √10, what is the simplified form of the fraction?

• 2√10

• √10/2

• 20√10

• 10√2

In the second example, what is the initial fraction given?

• 3 over 35√7

• 35 over 7

• 35 over 3

• 35 over 3√7

What do you multiply the numerator and denominator by to rationalize 35 over 3√7?

• Square root of 3

• 3

• Square root of 7

• 7

After rationalizing 35 over 3√7, what is the simplified form of the fraction?

• 35√7/21

• 3√7/5

• 7√5/3

• 5√7/3

Why is it important to write the fraction in its simplest form after rationalizing?

• To make calculations easier

• To ensure the fraction is accurate

• To reduce the size of the numbers

• To make the fraction more visually appealing

What is the result of multiplying the square root of 7 by itself?

• 21

• Square root of 49

• 7

• 14