Exploring Adding and Subtracting Rational Expressions

The video tutorial introduces the concept of adding and subtracting radicals. It outlines three main steps: simplifying radicals, identifying common radicals, and adding or subtracting their coefficients. The tutorial provides several example problems, ranging from basic to advanced, to illustrate these steps. It concludes with applications of radicals in geometry, such as calculating the perimeter of shapes using radical expressions.

What is the first step in adding and subtracting radicals?

• Add coefficients

• Subtract coefficients

• Identify common radicals

• Simplify all radicals

When adding or subtracting radicals, what must be the same for the radicals to be combined?

• Their bases

• Their exponents

• Their indices and radicands

• Their coefficients

In the example -2√20 - 2√5, what is the simplified form of -2√20?

• -8√5

• -4√5

• -6√5

• -2√5

What is the result of 3√6 - 2√6?

• 5√6

• 2√6

• √6

• 1√6

How do you simplify 10√7 + 2√63?

• 12√7

• 10√7 + 6√7

• 10√7 + 2√7

• 16√7

What is the simplified form of 2√32 - 3√8?

• 8√2 - 9√2

• 5√2

• 8√2 - 9√2

• 8√2 - 3√2

In the expression -4√160 - 2√90, what is the simplified form of -4√160?

• -8√10

• -12√10

• -20√10

• -16√10

What is the perimeter of a triangle with sides 2√72, 8√18, and 16√2 in simplest radical form?

• 60√2

• 52√2

• 48√2

• 36√2

How do you represent the perimeter of a rectangle with length 2√405 and width 9√48 in simplest radical form?

• 72√5 + 36√3

• 36√5 + 36√3

• 36√5 + 72√3

• 108√5 + 72√3

What is the simplified form of 8√45 + 6√5 + 30√2?

• 14√5 + 30√2

• 14√5 + 36√2

• 8√5 + 6√5 + 30√2

• 14√5 + 30√2