Rationalising The Denominator
Muhtasari
Surds are precise, but a square root lurking in a denominator makes an expression harder to read, harder to compare and harder to simplify. Rationalising the denominator is the technique that removes every irrational part from the bottom of a fraction, leaving a clean rational number underneath.
You will learn two core moves: multiplying by the surd itself when the denominator is a single term, and multiplying by the conjugate when it contains two terms. Both rest on one elegant algebraic fact: the product of conjugate surds is always rational. Master these and you will handle every rationalisation question Edexcel can set.
Malengo
- Rationalise the denominator of expressions involving surds
Maelezo ya Somo
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Tathmini ya Somo
Hongera kwa kukamilisha somo la Rationalising The Denominator. Sasa kwa kuwa umechunguza dhana na mawazo muhimu, ni wakati wa kuweka ujuzi wako kwa mtihani. Sehemu hii inatoa mazoezi mbalimbali maswali yaliyoundwa ili kuimarisha uelewaji wako na kukusaidia kupima ufahamu wako wa nyenzo.
Utakutana na mchanganyiko wa aina mbalimbali za maswali, ikiwemo maswali ya kuchagua jibu sahihi, maswali ya majibu mafupi, na maswali ya insha. Kila swali limebuniwa kwa umakini ili kupima vipengele tofauti vya maarifa yako na ujuzi wa kufikiri kwa makini.
Tumia sehemu hii ya tathmini kama fursa ya kuimarisha uelewa wako wa mada na kubaini maeneo yoyote ambapo unaweza kuhitaji kusoma zaidi. Usikatishwe tamaa na changamoto zozote utakazokutana nazo; badala yake, zitazame kama fursa za kukua na kuboresha.
- What is the conjugate of 3 + sqrt(5)? A) 3 + sqrt(5) B) 3 - sqrt(5) C) -3 + sqrt(5) D) -3 - sqrt(5) Answer: B
- Rationalise 1 / sqrt(2). Which is correct? A) sqrt(2) B) sqrt(2) / 4 C) sqrt(2) / 2 D) 2 / sqrt(2) Answer: C
- Which identity makes the conjugate method work? A) (a + b)^2 = a^2 + 2ab + b^2 B) (a + b)(a - b) = a^2 - b^2 C) a^2 + b^2 = (a + b)^2 D) (a - b)^2 = a^2 - 2ab + b^2 Answer: B
- What is 8 / (2 * sqrt(2)) in its simplest rationalised form? A) 2 * sqrt(2) B) 4 * sqrt(2) C) sqrt(2) D) 4 / sqrt(2) Answer: A
- Rationalise 1 / (sqrt(6) - sqrt(5)). The denominator becomes: A) 1 B) 11 C) sqrt(30) D) 6 - 5 Answer: A
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Pakua programu ya Green Bridge CBT kwenye simu yako au kompyuta yako ili kupata maelezo kamili ya masomo, maswali ya mazoezi, na mengi zaidi.
Inapatikana kwenye programu ya Green Bridge
Pakua programu ya Green Bridge CBT kwenye simu yako au kompyuta yako ili kupata maelezo kamili ya masomo, maswali ya mazoezi, na mengi zaidi.
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