Question

please solve this problem ​

Answer 1

$\small\red{\underline{Question = simplify \: the \: following \: expression }.} \\ \\ i) \: \: (5 + \sqrt{7} )(2 + \sqrt{5} ) \\ ii) \: \: (5 + \sqrt{5} )(5 - \sqrt{5} ) \\ iii) \: \: ( \sqrt{3} + \sqrt{7} ) {}^{2} \\ iv) \: \: (\sqrt{11} - \sqrt{7} )( \sqrt{11} + \sqrt{7} ) \\ \\ \small\orange{\underline{\underline{solution}}} \\ \\ \color{red} i) \: \: = (5 + \sqrt{7} )(2 + \sqrt{5} ) \\ \\ \color{green} = 10 + 5 \sqrt{5} + 2 \sqrt{7} + \sqrt{35} \: \: is \: th e\: answer \\ \\ \color{red}ii) = \: \: (5 + \sqrt{5} )(5 - \sqrt{5} ) \\ \\ \color{blue} = {5}^{2} - ( \sqrt{5} ) {}^{2} \\ \\ \color{blue} = 25 - 5 \\ \\ \color{green} = 20 \: \: is \: the \: answer \\ \\ \color{red}iii) \: = \: ( \sqrt{3} + \sqrt{7} ) {}^{2} \\ \\ \color{blue} = ( \sqrt{3} ) {}^{2} + 2( \sqrt{3} )( \sqrt{7} ) + ( \sqrt{7} ) {}^{2} \\ \\\color{blue} = 3 + 2 \sqrt{21} + 7 \\ \\ \color{green} = 10 + 2 \sqrt{21} \: \: is \: the \: answer \\ \\ \color{red} iv) \: = \: (\sqrt{11} - \sqrt{7} )( \sqrt{11} + \sqrt{7} ) \\ \\ \color{blue} = (\sqrt{11} ) {}^{2} - (\sqrt{7} ) {}^{2} \\ \\ \color{blue} = 11 - 7 \\ \\ \color{green} = 4 \: \: is \: the \: answer \\ \\\color{purple} hope \: its \: help \: you \: dear \: \\ \\ \small\pink{\boxed{\boxed{it's ᭄亗 乄 ＭꫝղᎥនh 乄 亗✯❤࿐}}}$

Answer 2

Answer:

here example 16 , this is from my math book