Surds and Rationalizing Denominators Quiz

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

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.