Question

Rationalise 1 + root 2 / 2 - root 2

Answer 1

⠀⠀⠀⠀⠀⠀${\rm{\purple{\underline{\underline{★Required \:Answer★}}}}}$

$\longmapsto \frac{4 + 3 \sqrt{2} }{2}$

⠀⠀⠀${\rm{\red{\underline{\underline{★Given \: Equation ★}}}}}$

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

⠀⠀⠀⠀⠀${\rm{\pink{\underline{\underline{★Solution★}}}}}$

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

$\longmapsto\frac{1 + \sqrt{2} }{2 - \sqrt{2} } \times \frac{2 + \sqrt{2} }{2 + \sqrt{2} }$

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

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

$\longmapsto \frac{4 + 3 \sqrt{2} }{4 - 2}$

$\longmapsto \frac{4 + 3 \sqrt{2} }{2}$