Question

please answer 95 no.

Answer 1

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


Splitting 3 in two positive number.

3 = 2 + 1


$\sqrt{2 + 1 + 2 \sqrt{2} } - \sqrt{2 + 1 - 2 \sqrt{2} }$


$\sqrt{( { \sqrt{2} )}^{2} + ( \sqrt{1} ) {}^{2} + 2 \sqrt{2}} - \sqrt{( \sqrt{2} ) {}^{2} + ( \sqrt{1}) {}^{2} - 2 \sqrt{2} \: \: \: }$



Indentity 1 : a² + b² + 2ab = ( a + b )²

Indentity 2 : a² + b² - 2ab = ( a - b )²



$\sqrt{( \sqrt{2} + 1) {}^{2} } - \sqrt{( \sqrt{2} - 1) {}^{2} } \\ \\ \\ \sqrt{2} + 1 -( \sqrt{2} - 1) \\ \\ \\ \sqrt{2} + 1 - \sqrt{2} + 1 \\ \\\\ 2$




Therefore the value of $\sqrt{3 + 2 \sqrt{2} } - \sqrt{3 - 2 \sqrt{2} }$ is 2