Question

rationalize the dinominator 1 by 3-root 2
$\frac{1}{3 - \sqrt{2} }$
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Answer 1

Answer:

$\frac{1}{3-\sqrt{2} }$

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

$\frac{3+\sqrt{2}}{3^2-(\sqrt{2})^2 }$

$\frac{3+\sqrt{2}}{9-2 }$

$\frac{3+\sqrt{2}}{7}$

Answer 2

$\large\bf\underline\red{Answer \: :-}$

$\sf\leadsto{ \frac{1}{3 - \sqrt{2} } \times \frac{3 + \sqrt{2} }{3 + \sqrt{2} } } \\ \\ \sf\leadsto{ \frac{3 + \sqrt{2} }{(3 - \sqrt{2})(3 + \sqrt{2}) } }$

Using (a+b) (a-b) = a² - b²

$\sf\leadsto{ \frac{3 + \sqrt{2} }{(3) {}^{2} - ( \sqrt{2}) {}^{2} } } \\ \\ \sf\leadsto{ \frac{3 + \sqrt{2} }{9 - 2} } \\ \\ \sf\leadsto{ \frac{3 + \sqrt{2} }{7} }$

Required

${\large{\leadsto{\underline{\boxed{\bf{\red{ \frac{3 + \sqrt{2} }{7} }}}}}}}$

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