Further Pure Mathematics - 4PM1 PearsonEdexcel

Surds

Gbogbo ọrọ náà

Every calculator gives you a decimal approximation, but mathematics often demands an exact answer. Surds let you keep square roots in their precise form, and learning to simplify, combine and rationalise them is one of the most rewarding algebraic skills you will develop in this course.

This topic shows you how to simplify surds by extracting square factors, how to multiply and divide them, and how to eliminate an irrational denominator using conjugate pairs. These techniques surface throughout the rest of the 4PM1 syllabus, from solving quadratics to working with trigonometric exact values.

Ebumnobi

Understand what surds represent and their use for exact answers
Perform simple manipulation of surds

Maapụ uche

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Akwụkwọ Ọmụmụ

When you type a square root into a calculator you get a string of digits that goes on and on. That decimal is an approximation. In pure mathematics, leaving your answer as a surd preserves total accuracy, and examiners expect you to do exactly that whenever a question says 'give an exact answer'.

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Nnyocha Ọmụmụ

Ekele diri gi maka imecha ihe karịrị na Surds. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.

Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.

Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.

Which of the following is a surd? A) sqrt(16) B) sqrt(25) C) sqrt(10) D) sqrt(49) Answer: C
Simplify sqrt(75). A) 5 sqrt(3) B) 3 sqrt(5) C) 25 sqrt(3) D) 15 Answer: A
What is (3 + sqrt(2))(3 - sqrt(2))? A) 7 B) 9 C) 11 D) 9 - sqrt(2) Answer: A
Simplify sqrt(8) + sqrt(18). A) sqrt(26) B) 5 sqrt(2) C) 4 sqrt(2) D) 6 sqrt(2) Answer: B
Which expression is equivalent to sqrt(a) times sqrt(b)? A) sqrt(a + b) B) sqrt(a - b) C) sqrt(ab) D) a sqrt(b) Answer: C

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