tex]...

July 2022 1 10 Report

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[tex] \sqrt{2x} - \sqrt{3y} + \sqrt{2y} - \sqrt{3x}

\sqrt[3]{ a^{4} } + \sqrt[3]{a b^{3} } - \sqrt[3]{ a^{3}b } - \sqrt[3]{ b^{4} }

\sqrt[4]{m} - \sqrt[8]{m} - 6

\sqrt[5]{a} + 7 \sqrt[10]{a} + 12[/tex]

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Artem112

Verified answer

$\sqrt{2x} - \sqrt{3y} + \sqrt{2y} - \sqrt{3x} = \sqrt{2}( \sqrt{x}+ \sqrt{y} - \sqrt{3}( \sqrt{y} +\sqrt{x})= \\\ =( \sqrt{y} +\sqrt{x})( \sqrt{2} -\sqrt{3})$

$\sqrt[3]{ a^{4} } + \sqrt[3]{a b^{3} } - \sqrt[3]{ a^{3}b } - \sqrt[3]{ b^{4} } =
\sqrt[3]{ a^3 } (\sqrt[3]{ a }-\sqrt[3]{ b })+ \sqrt[3]{b^{3} } (\sqrt[3]{ a }-\sqrt[3]{ b })=
\\\
 (\sqrt[3]{ a }-\sqrt[3]{ b }) (a+b)$

$\sqrt[4]{m} - \sqrt[8]{m} - 6= \sqrt[4]{m} - 3\sqrt[8]{m} +2\sqrt[8]{m}- 6= \\\ =
 \sqrt[8]{m}( \sqrt[8]{m} - 3)+2(\sqrt[8]{m}- 3)=(\sqrt[8]{m}- 3)(\sqrt[8]{m}+2)
$

$\sqrt[5]{a} + 7 \sqrt[10]{a} + 12= \sqrt[5]{a} + 3 \sqrt[10]{a} + 4 \sqrt[10]{a}+ 12=
\\\ =\sqrt[10]{a}( \sqrt[10]{a} + 3 ) + 4( \sqrt[10]{a} + 3 ) =
( \sqrt[10]{a} + 3 ) (( \sqrt[10]{a} + 4 )$

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