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Simplify (\(\sqrt2 + \frac{1}{\sqrt3})(\sqrt2 - \frac{1}{\sqrt3}\))


Question

Simplify (\(\sqrt2 + \frac{1}{\sqrt3})(\sqrt2 - \frac{1}{\sqrt3}\))

Options

A) \(\frac{7}{3}\)

B) \(\frac{5}{3}\)

C) \(\frac{5}{2}\)

D) \(\frac{3}{2}\)

The correct answer is B.

Explanation:

(\(\sqrt2 + \frac{1}{\sqrt3})(\sqrt2 - \frac{1}{\sqrt3}\))
\(\sqrt4 - \frac {\sqrt2}{\sqrt3} + \frac {\sqrt2}{\sqrt3} - \frac {1}{\sqrt9}\)
= 2 - \(\frac {1}{3}\)
= \(\frac {16 - 1}{3}\)
= \(\frac{5}{3}\)

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Dicussion (1)

  • (\(\sqrt2 + \frac{1}{\sqrt3})(\sqrt2 - \frac{1}{\sqrt3}\))
    \(\sqrt4 - \frac {\sqrt2}{\sqrt3} + \frac {\sqrt2}{\sqrt3} - \frac {1}{\sqrt9}\)
    = 2 - \(\frac {1}{3}\)
    = \(\frac {16 - 1}{3}\)
    = \(\frac{5}{3}\)

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