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Operations on Irrational Number

Express the f...

Question

Express the following with rational denominator:

$(i) \frac{1}{3 + \sqrt{2}}$

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Solution

Given: $\frac{1}{3 + \sqrt{2}}$
Multiplying and dividing given number by
$3 - \sqrt{2}$
$= \frac{3 - \sqrt{2}}{(3 + \sqrt{2}) (3 - \sqrt{2})}$
$= \frac{3 - \sqrt{2}}{(3)^{2} - (\sqrt{2})^{2}}$
Using identity $(a + b) (a - b) = a^{2} - b^{2}$
$= \frac{3 - \sqrt{2}}{9 - 2}$
$= \frac{3 - \sqrt{2}}{7}$

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Operations on Irrational Number

Standard IX Mathematics

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