Question

4( 1+√2)/1-√2 is it rational or irrational please gI've me step by step solution​​

Answer 1

$\small\red{\boxed{Question = \frac{4(1 + \sqrt{2} )}{1 - \sqrt{2} } }.} \\ \\ \small\orange{\underline{ \underline{solution}: - }} \\ \\ \color{blue} = \frac{4(1 + \sqrt{2}) }{1 - \sqrt{2} } \\ \\ \color{blue} = \frac{4 + 4 \sqrt{2} \times 1 + \sqrt{2} }{1 - \sqrt{2} \times 1 + \sqrt{2} } \\ \\ \color{blue} = \frac{4 + 4 \sqrt{2} + 4 \sqrt{2} + 8 }{ {1}^{2} - {( \sqrt{2} )}^{2} } \\ \\ \color{blue} = \frac{12 + 8 \sqrt{2} }{1 - 2} \\ \\ \color{blue} = \frac{(12 + 8 \sqrt{2}) \times - 1 }{ - 1 \times - 1} \\ \\ \color{blue} = \frac{ - 12 - 8 \sqrt{2} }{1} \\ \\ \color{green} = - 12 - 8 \sqrt{2} \: \: \: this \: is \: a \: rational \: . \\ \\ \\ \small\orange{\underline{ \underline{Hope \: It's \: Help \: You }: - }} \\ \\ \small\red{\boxed{\boxed{it's ᭄亗 乄 ＭꫝղᎥនh 乄 亗✯❤࿐} }}$

Answer 2

$\huge \fbox \blue{a} \fbox \purple{n} \fbox \green{s} \fbox \red{w} \fbox \pink{e} \fbox \orange{r}$

$\huge\tt\: \red{ = \: \frac{4(1 \: + \: \sqrt{2})}{1 \: - \: \sqrt{2} } }$

$\huge\tt \red{ = \: \frac{4 \: + \: 4 \sqrt{2} \: \times \: 1 \: + \: \sqrt{2} } {1 \: - \sqrt{2} \: \times \: 1 \: + \: \sqrt{2}}}$

$\huge\tt\red{\frac{ = \: 4 \: + \: 4 \: \sqrt{2} \: + \: 4 \sqrt{2} \: + \: 8}{{1}^{2} \: - \: ( \sqrt{2})^{2} }}$

$\huge\tt\red{\frac{ = \: 12 \: + \: 8 \sqrt{2} }{1 \: - \: 2}}$

$\huge\tt\red{= \: \frac{(12 \: + \: 8 \sqrt{2)} \: \times \: - 1 }{ - 1 \: \times \: - 1}}$

$\huge\tt\red{= \: \frac{12 \: - \: 8 \sqrt{2} }{1}}$

$\huge\tt\red{ \therefore - 12 \: - 8 \sqrt{2} }$