Mathematics (9-1) - 0980 CIE

Surds

Bayani Gaba-gaba

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.

Manufura

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

Takardar Darasi

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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Nazarin Darasi

Barka da kammala darasi akan Surds. Yanzu da kuka bincika mahimman raayoyi da raayoyi, lokaci yayi da zaku gwada ilimin ku. Wannan sashe yana ba da ayyuka iri-iri Tambayoyin da aka tsara don ƙarfafa fahimtar ku da kuma taimaka muku auna fahimtar ku game da kayan.

Za ka gamu da haɗe-haɗen nau'ikan tambayoyi, ciki har da tambayoyin zaɓi da yawa, tambayoyin gajeren amsa, da tambayoyin rubutu. Kowace tambaya an ƙirƙira ta da kyau don auna fannoni daban-daban na iliminka da ƙwarewar tunani mai zurfi.

Yi wannan ɓangaren na kimantawa a matsayin wata dama don ƙarfafa fahimtarka kan batun kuma don gano duk wani yanki da kake buƙatar ƙarin karatu. Kada ka yanke ƙauna da duk wani ƙalubale da ka fuskanta; maimakon haka, ka kallesu a matsayin damar haɓaka da ingantawa.

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

Akwai a cikin manhajar Green Bridge

Zazzage manhajar Green Bridge CBT a wayar ka ko kwamfyuta ka don samun cikakkiyar bayanan darasi, tambayoyin aiki, da ƙari.

Cikakkiyar bayanan darasi tare da zane-zane
Mataimakiyar koyo da AI
Yi karatu ba tare da intanet ba, a kowane lokaci, a ko'ina
Akwai a Android, Windows, macOS, da Linux

Akwai a cikin manhajar Green Bridge

Zazzage manhajar Green Bridge CBT a wayar ka ko kwamfyuta ka don samun cikakkiyar bayanan darasi, tambayoyin aiki, da ƙari.

Cikakkiyar bayanan darasi tare da zane-zane
Mataimakiyar koyo da AI
Yi karatu ba tare da intanet ba, a kowane lokaci, a ko'ina
Akwai a Android, Windows, macOS, da Linux

Yi Aikin Tambayoyin Gwaji

Kana son yin aikin tambayoyin gwaji kan Surds? Sauke manhajar Green Bridge CBT don samun tambayoyin gwaji da cikakkun jarrabawa akan wannan batu.

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