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# Surds and Rationalizing Denominators Quiz

Created by
@EndearingPointOfView

## Questions and Answers

### What is the sum of angles Zc and Zd if they intersect on the side where Ze and d are formed?

• 180° (correct)
• 90°
• 120°
• 45°
• ### Which of the following is an example of a surd?

• √51 (correct)
• 5/2
• 4
• √16
• ### What is the result of simplifying √√27?

• 3√3 (correct)
• 3√2
• √3
• 3√√3
• ### What is the product of 3√12 and √√18 when simplified to simplest form?

<p>6√6</p> Signup and view all the answers

### Which pair consists of like surds?

<p>5√5, √75</p> Signup and view all the answers

### What is the simplest form of the division result between √39 and 1?

<p>-1/√39</p> Signup and view all the answers

## Study Notes

### Properties of Lines and Surds

• Two lines l and m intersect on the side of the transversal where ∠Z and ∠d are formed.
• ∠Zc + ∠Zd = 180° is impossible, leaving one remaining possibility.

### Rationalizing Denominators

• Rationalizing factors are used to rationalize denominators.
• Numbers with rational denominators can be used to simplify expressions.

### Ordering Surds

• The order of surds is determined by the value of the number under the square root.

### Identifying Surds

• √51 is a surd.
• √16 is not a surd (it can be simplified to 4).
• √ISI is not a defined mathematical expression.
• √256 is not a surd (it can be simplified to 16).

### Simplifying Surds

• √√27 = √3
• √√50 = √10
• √250 = √25√10 = 5√10

### Classifying Surds

• Like surds: √52 and 5√13 (both have the same radicand, 13)
• Unlike surds: √68 and 5√3 (different radicands)
• Like surds: 4√18 and 7√2 (both have the same radicand, 2)
• Unlike surds: 19√12 and 6√3 (different radicands)
• Like surds: 5√22 and 7√33 (both have the same radicand, 11)
• Unlike surds: 5√5 and √75 (different radicands)

### Comparing Surds

• 7√2 > 5√3
• √247 < √274
• 5√5 > 7√2
• 4√42 < 9√2
• √39 = √(3^2 × 13) = 3√13

### Rationalizing Denominators

• Rationalize the denominator: 3√5/parth_k
• Rationalize the denominator: (9√5 - 4√5 + √125) / 3
• Rationalize the denominator: (√7 - 2²/2√7 + 2√7) / 5

### Multiplying and Dividing Surds

• 3√12 × √18 = 3√216 = 36
• 3√12 × 7√15 = 21√180
• 3√8 × √5 = √120
• 5√8 × 2√8 - 1 = 10√16 - 1
• √39 ÷ √39 = 1

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## Description

Test your knowledge on surds and rationalizing denominators with this quiz. Questions include identifying the order of given surds and determining which expressions are surds. Explore concepts such as intersection of lines and angles in the context of surds.

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