Đáp án:
$c)-\dfrac{21}{\sqrt{2}}|a-b|b^2|c|\\ d)12-18\sqrt{2}+16\sqrt{3}\\ e)|ab|+2|b|-\sqrt{a^2+\sqrt{ab}}\\ g)a^3b.m.\left|\dfrac{n}{m}\right|-a^3b^3\sqrt{\dfrac{m}{n}}+a^4$
Giải thích các bước giải:
$c)-\dfrac{2}{3}\sqrt{\dfrac{(a-b)^3.b^5}{c}}.\dfrac{9}{4}\sqrt{\dfrac{c^3}{2(a-b)}}.\sqrt{98b}\\ =-\dfrac{2}{3}.\dfrac{9}{4}.\sqrt{98}\sqrt{\dfrac{(a-b)^3.b^5}{c}.\dfrac{c^3}{2(a-b)}.b}\\ =-\dfrac{3}{2}.7\sqrt{2}\sqrt{(a-b)^2.b^4.c^2}\\ =-\dfrac{21}{\sqrt{2}}|a-b|b^2|c|\\ d)\left(\sqrt{6}-3\sqrt{3}+5\sqrt{2}-\dfrac{1}{2}\sqrt{8}\right).2\sqrt{6}\\ =\sqrt{6}.2\sqrt{6}-3\sqrt{3}.2\sqrt{6}+5\sqrt{2}.2\sqrt{6}-\dfrac{1}{2}\sqrt{8}.2\sqrt{6}\\ =2.6-6\sqrt{18}+10\sqrt{12}-\sqrt{48}\\ =12-6\sqrt{2.9}+10\sqrt{4.3}-\sqrt{16.3}\\ =12-18\sqrt{2}+20\sqrt{3}-4\sqrt{3}\\ =12-18\sqrt{2}+16\sqrt{3}\\ e)\left(\sqrt{ab}+2\sqrt{\dfrac{b}{a}}-\sqrt{\dfrac{a}{b}+\sqrt{\dfrac{1}{ab}}}\right).\sqrt{ab}\\ =\sqrt{ab}.\sqrt{ab}+2\sqrt{\dfrac{b}{a}}.\sqrt{ab}-\sqrt{ab}\sqrt{\dfrac{a}{b}+ab\sqrt{\dfrac{1}{ab}}}\\ =\sqrt{(ab)^2}+2\sqrt{\dfrac{b}{a}.ab}-\sqrt{\dfrac{a}{b}.ab+ab\sqrt{\dfrac{1}{ab}}}\\ =|ab|+2\sqrt{b^2}-\sqrt{a^2+\sqrt{ab}}\\ =|ab|+2|b|-\sqrt{a^2+\sqrt{ab}}\\ g)\left(\dfrac{am}{b}\sqrt{\dfrac{n}{m}}-\dfrac{ab}{n}\sqrt{mn}+\dfrac{a^2}{b^2}\sqrt{\dfrac{m}{n}}\right).a^2b^2.\sqrt{\dfrac{n}{m}}\\ =\dfrac{am}{b}\sqrt{\dfrac{n}{m}}.a^2b^2.\sqrt{\dfrac{n}{m}}-\dfrac{ab}\\{n}\sqrt{mn}.a^2b^2.\sqrt{\dfrac{n}{m}}+\dfrac{a^2}{b^2}\sqrt{\dfrac{m}{n}}.a^2b^2.\sqrt{\dfrac{n}{m}}\\ =a^3b.m.\sqrt{\dfrac{n^2}{m^2}}-a^3b^3\sqrt{\dfrac{m}{n}}+a^4\\ =a^3b.m.\left|\dfrac{n}{m}\right|-a^3b^3\sqrt{\dfrac{m}{n}}+a^4$
