Question

by rationalising the denominator find the value of the two significant figures. please step by step explains
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Answer 1

Step-by-step explanation:

1)

$\frac{1}{3 - \sqrt{2} } \\ \\ \frac{1}{3 - \sqrt{2} } \times \frac{3 + \sqrt{2} }{3 + \sqrt{2} } \\ \\ \frac{3 + \sqrt{2} }{ {3}^{2} - { \sqrt{2} }^{2} } \\ \\ \frac{3 + \sqrt{2} }{9 - 2} \\ \\ \frac{3 + \sqrt{2} }{7}$

2)

$\frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ \frac{2 - \sqrt{3} }{ {2}^{2} - { \sqrt{3} }^{2} } \\ \\ \frac{2 - \sqrt{3} }{4 - 3} \\ \\ 2 - \sqrt{3}$

3)

$\frac{4}{3 \sqrt{2 - \: \: 2 \sqrt{3} } } \\ \\ \frac{4}{3 \sqrt{2} - 2 \sqrt{3} } \times \frac{3 \sqrt{2 } +2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } \\ \\ \frac{4(3 \sqrt{2} + 2 \sqrt{3} )}{ {3 \sqrt{2} }^{2} - {2 \sqrt{3} }^{2} }$