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Simplify $\frac{1}{3-√2}$ in the form of p + q&radic...

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.

$\frac{3}{7}$ + $\frac{√2}{7}$

View answer & explanation

Correct answer is D

Rationalization with conjugate ${3+√2}$

$\frac{1}{3-√2}$

→ $\frac{1 * [3+√2]}{[3-√2][3+√2]}$

= $\frac{3+√2}{9 -3√2 + 3√2 + √4}$

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

= $\frac{3}{7}$ + $\frac{√2}{7}$

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