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Bentuk sederhana dari 2/(3+√2) adalah…

Bentuk sederhana dari 2/(3+√2) adalah…
A. (6+2√2)/7
B. (6-2√2)/7
C. (5+√2)/2
D. (5-√2)/2

Jawaban : B

Ingat!
merasionalkan bentuk akar
a/(b + √c)
= a/(b + √c) × (b – √c) /(b – √c)

a² – b² = (a + b) (a-b)

Perkalian distributif
a × (b + c) = (a × b) + (a ×c)

Pembahasan
2/(3+√2) × (3-√2) /(3-√2)
= [2 (3-√2) ]/[(3+√2) (3-√2) ] = [6 – 2√2]/[3² – (√2)²] = [6 – 2√2]/[9 – 2] = [6 – 2√2]/7

Jadi, bentuk sederhana dari 2/(3+√2) adalah [6 – 2√2]/7

Oleh karena itu, jawaban yang benar adalah B

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