Rationalise \(\frac{\sqrt{2}}{3 + \sqrt{2}}\)
A
\(\frac{3\sqrt{2} - 2}{7}\)
B
\(\frac{3\sqrt{2} + 2}{7}\)
C
\(\frac{3\sqrt{2}}{7}\)
D
\(\frac{\sqrt{2}}{5}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
To rationalise \(\frac{\sqrt{2}}{3 + \sqrt{2}}\), multiply both the numerator and denominator of the fraction
by the conjugate of the denominator, that is, 3 - \(\sqrt{2}\)
\(\frac{\sqrt{2}}{3 + \sqrt{2}}\) x \(\frac{3 - \sqrt{2}}{3 - \sqrt{2}}\)
= \(\frac{3\sqrt{2} - 2}{9 - 2}\) = \(\frac{3\sqrt{2} - 2}{7}\)
Source: Myschool Past Questions Archive (Record #78165)