Surds and Rationalizing Denominators Quiz

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