Question

rationalize 3 + 2 root 2 + 1 upon 3 + 2 root 2​

Answer 1

Given :- (3 + 2√2 + 1)/(3 + 2√2)

Here, we've to rationalize the denominator

$\sf = \frac{3 + 2 \sqrt{2} + 1}{3 + 2 \sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } \\ \\ \sf = \frac{(3 + 2 \sqrt{2} + 1)(3 - 2 \sqrt{2} )}{(3 + 2 \sqrt{2})(3 - 2 \sqrt{2} )} \\ \\ \sf = \frac{3(3 + 2\sqrt{2} + 1) - 2\sqrt{2}(3 +2\sqrt{2} + 1)}{{(3)}^{2} - ( {2 \sqrt{2} })^{2}} \\ \\ \sf =\frac{9 + 6 \sqrt{2} + 3 - 6 \sqrt{2} - 8 - 2 \sqrt{2} }{9 - 8 } \\ \\ \sf = \frac{4 - 2 \sqrt{2} }{1} \\ \\ \sf = \boxed{4 - 2 \sqrt{2} }$

Answer 2

Answer:

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