Question

Simplify 1/1+2√2-√3


Please solve it fast accurate

​

Answer 1

is this accuracy enough?

thanks for asking

Answer 2

Answer:-

$\dfrac{1}{1 + 2 \sqrt{2} + \sqrt{3} } \times \dfrac{1 + 2 \sqrt{2} - \sqrt{3} }{1 + 2 \sqrt{2 } - \sqrt{3} }$

$\quad$

$\dfrac{1 + 2 \sqrt{2} - \sqrt{3} }{(1 + 2 \sqrt{2} ) {}^{2} - (3) {}^{2} } = \dfrac{1 + 2 \sqrt{2} - \sqrt{3} }{1 + 8 + 4 \sqrt{2} - 3 }$

$\quad$

$= \dfrac{1 + 2 \sqrt{2} - \sqrt{3} }{6 + 4 \sqrt{2} } \times \dfrac{6 - 4 \sqrt{2} }{6 - 4 \sqrt{2} }$

$\quad$

$= \dfrac{6 - 4 \sqrt{2} + 12 \sqrt{2} - 16 - 6 \sqrt{3} + 4 \sqrt{6} }{36 - 32}$

$\quad$

$= \dfrac{ - 10 + 8 \sqrt{2} - 6 \sqrt{3} + 4 \sqrt{6} }{4}$

$\quad$

$= \dfrac{ - 5 + 4 \sqrt{2} - 3 \sqrt{3} + 2 \sqrt{6} }{2}$