Старонка:Элемэнтарная альгэбра (1922―1924). Частка II.pdf/36

ПРЫКЛАД I.

$7{\sqrt {2ax^{2}}}-3{\sqrt {5ab}}+({\sqrt {3b}}-4{\sqrt {2ax^{2}}})-(3{\sqrt {5ab}}+11{\sqrt {3b}}-8{\sqrt[{3}]{2ax^{2}}})=$
$=7{\sqrt[{3}]{2ax^{2}}}-3{\sqrt {5ab}}+{\sqrt {3b}}-4{\sqrt[{3}]{2ax^{2}}}-3{\sqrt {5ab}}-11{\sqrt {3b}}+8{\sqrt[{3}]{2ax^{2}}}=$
$=11{\sqrt[{3}]{2ax^{2}}}-6{\sqrt {5ab}}-8{\sqrt {3b}}$

ПРЫКЛАД II.

$3{\sqrt {\dfrac {an}{4}}}-{\bigg (}{\dfrac {16}{a}}{\sqrt {\dfrac {a^{3}n}{16}}}-3a{\sqrt {\dfrac {n}{a}}}+2n{\sqrt {\dfrac {a}{9n}}}{\bigg )}=3{\sqrt {\dfrac {an}{4}}}-{\dfrac {16}{3a}}{\sqrt {\dfrac {a^{3}n}{16}}}+$

$+3a{\dfrac {n}{a}}-2n{\sqrt {\dfrac {a}{9n}}}={\dfrac {3}{2}}{\sqrt {an}}-{\dfrac {16}{3a\cdot 4}}{\sqrt {a^{2}\cdot {an}}}+3a{\sqrt {\dfrac {an}{a^{2}}}}-2n{\sqrt {\dfrac {an}{9n^{2}}}}=$

$={\dfrac {3}{2}}{\sqrt {an}}-{\dfrac {4a}{3a}}{\sqrt {an}}+{\dfrac {3a}{a}}{\sqrt {an}}-{\dfrac {2n}{3n}}{\sqrt {an}}={\dfrac {3}{2}}{\sqrt {an}}-{\dfrac {4}{3}}{\sqrt {an}}+$

$+3{\sqrt {an}}-{\dfrac {2}{3}}{\sqrt {an}}=2{\dfrac {1}{2}}{\sqrt {an}}$

Задачы.

Выканаць дзеяньні і упросьціць.

184.	${\sqrt {117}}+{\sqrt {325}})-({\sqrt {52}}-{\sqrt {1573}})$
185.	$({\sqrt[{3}]{16}}+{\sqrt[{3}]{128}})+({\sqrt[{3}]{250}}-{\sqrt[{3}]{54}})$
186.	$3({\sqrt[{3}]{135}}+4{\sqrt[{3}]{40}})+6{\sqrt[{3}]{320}}-{\sqrt[{3}]{625}})$
187.	$6a{\sqrt {63ab^{3}}}-3{\sqrt {112a^{3}b^{3}}}+2ab{\sqrt {343ab}}-5b{\sqrt {28a^{3}b}})$
188.	$3{\sqrt[{5}]{2}}-{\dfrac {1}{2}}{\sqrt[{5}]{64}}+10{\sqrt[{5}]{486}}-6{\dfrac {1}{2}}{\sqrt[{5}]{2}})$
189.	$3{\dfrac {1}{2}}{\sqrt {24}}-{\dfrac {\sqrt[{3}]{54}}{4}}+2{\dfrac {\sqrt {99}}{3}}-1{\dfrac {1}{2}}{\sqrt {44}})+3{\sqrt[{3}]{2}}$
190.	${\sqrt[{4}]{162x^{4}y}}-{\sqrt[{3}]{54x^{3}y}}-{\sqrt[{4}]{32x^{8}y^{5}}}+{\sqrt[{3}]{16x^{6}y^{4}}})$
191.	$5{\sqrt[{3}]{x^{2}y^{5}}}+4y^{2}{\sqrt {\dfrac {x^{2}}{y}}}+{\dfrac {4y}{x^{2}}}{\sqrt[{3}]{-x^{8}y^{2}}}-{\Bigg (}6xy{\sqrt[{3}]{\dfrac {y^{2}}{x}}}+{\dfrac {3}{2}}xy^{2}{\sqrt[{3}]{-{\dfrac {8}{xy}}}}{\Bigg )}$
192.	${\sqrt {\dfrac {(a^{2}-b^{2})(a-b)^{2}}{a+b}}}+{\dfrac {1}{2a-3b}}{\sqrt {(2a-3b)^{2}(a-b)}}-$ $-(a-b){\sqrt {\dfrac {(a+b)^{2}}{a-b}}}$