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Simplify \(\frac{1}{3-√2}\) in the form of p + q√2

Mathematics
JAMB 2022

Simplify \(\frac{1}{3-√2}\) in the form of p + q√2

  • A. \(\frac{7}{3}\) - \(\frac{1}{7√2}\)
  • B. \(\frac{7}{3}\) + \(\frac{1}{7√2}\)
  • C. \(\frac{3}{7}\) - \(\frac{1}{7√2}\)
  • D. \(\frac{3}{7}\) + \(\frac{√2}{7}\)
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Correct Answer: Option D
Explanation

Rationalization with conjugate \({3+√2}\)

 \(\frac{1}{3-√2}\)

→ \(\frac{1 * [3+√2]}{[3-√2][3+√2]}\)

=  \(\frac{3+√2}{9 -3√2 + 3√2 - √4}\)

=  \(\frac{3+√2}{9 - 2}\) →  \(\frac{3+√2}{7}\)

= \(\frac{3}{7}\) +  \(\frac{√2}{7}\)

There is an explanation video available below.


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Explanation Video

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