Simplify \(\frac{1}{3-√2}\) in the form of p + q√2
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Correct Answer: Option D
Explanation:
Rationalization withconjugate \({3+√2}\)
\(\frac{1}{3-√2}\)
→\(\frac{1 * [3+√2]}{[3-√2][3+√2]}\)
=\(\frac{3+√2}{9 -3√2 +3√2 + √4}\)
=\(\frac{3+√2}{9 -2}\)→\(\frac{3+√2}{7}\)
=\(\frac{3}{7}\) +\(\frac{√2}{7}\)
Rationalization withconjugate \({3+√2}\)
\(\frac{1}{3-√2}\)
→\(\frac{1 * [3+√2]}{[3-√2][3+√2]}\)
=\(\frac{3+√2}{9 -3√2 +3√2 + √4}\)
=\(\frac{3+√2}{9 -2}\)→\(\frac{3+√2}{7}\)
=\(\frac{3}{7}\) +\(\frac{√2}{7}\)