Question

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Answer 1

${\large{\pmb{\sf{\underline{RequirEd \; Solution...}}}}}$

⋆ It is given that we have to simplify the two given expressions that are

${\sf{\star \: (2+\sqrt{3})(2-\sqrt{3})}}$

⠀⠀⠀⠀━━━━━━━━━━━━━━

${\sf{\star \: (\sqrt{2} + \sqrt{5})(3-\sqrt{5})}}$

⋆ Now let us simpily them step by step in a proper way. Let's do it!

~ Firstly solving part 1)

$:\implies \sf (2+\sqrt{3})(2-\sqrt{3}) \\ \\ \sf To \: solve \: this, \: we \: have \: to \: use \: identity \\ \\ \sf Using \: identity \: is \: mentioned \: below \leadsto \\ \\ \sf (a-b)(a+b) = a^2 - b^2 \\ \\ \sf According \: to \: the \: identity \\ \\ \sf Here, \: a \: is \: 2 \: and \: b \: is \sqrt{3} \\ \\ \sf By \: using \: identity \: we \: get \\ \\ :\implies \sf (2)^{2} - (\sqrt{3})^{2} \\ \\ :\implies \sf 4 - 3 \\ \\ :\implies \sf 1 \\ \\ {\pmb{\sf{Hence, \: 1 \: is \: our \: requied \: solution!}}}$

~ Solving part 2) now

$:\implies \sf (\sqrt{2} + \sqrt{5})(3-\sqrt{5}) \\ \\ :\implies \sf \sqrt{2}(3-\sqrt{5}) + \sqrt{5}(3-\sqrt{5}) \\ \\ :\implies \sf 3\sqrt{2} - \sqrt{10} + 3\sqrt{5} - \sqrt{25} \\ \\ {\pmb{\sf{Henceforth, \: 3\sqrt{2} - \sqrt{10} + 3\sqrt{5} - \sqrt{25} \: is \: requied \: solution!}}}$