Mathematics - International - 0607 CIE

Surds

Gbogbo ọrọ náà

A surd is a root that cannot be simplified to a whole number, such as \(\sqrt{2}\) or \(\sqrt{5}\). Surds let you keep answers exact rather than rounding, which matters whenever a question asks for an exact value, and they are the natural language of Pythagoras and trigonometry results.

In this lesson (Extended tier) you will simplify surds, multiply and add them where possible, and rationalise a denominator so that no surd is left underneath a fraction. These techniques keep working tidy and answers exact.

Ebumnobi

Understand and use surds, including simplifying expressions.
Rationalise the denominator.

Akọmọ Ojú-ẹkọ

Writing \(\sqrt{50}\) as \(5\sqrt{2}\) is both neater and exact, and leaving an answer as a surd avoids the rounding error a decimal would introduce. Surds appear throughout geometry and trigonometry, so handling them confidently keeps later work exact.

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Ayẹwo Ẹkọ

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.

Simplify √50. A. 5√2 B. 2√5 C. 25√2 D. 10√5 Answer: A
Work out √3 x √12. A. √15 B. 6 C. 36 D. 4√3 Answer: B
Simplify 2√5 + 3√5. A. 5√10 B. 6√5 C. 5√5 D. 5 Answer: C
Rationalise the denominator of 1/√2. A. √2 B. 2/√2 C. √2/2 D. 1/2 Answer: C
Which expression cannot be simplified? A. √8 B. √2 + √3 C. √2 x √8 D. 4√3 - √3 Answer: B