Đáp án:
$a)\dfrac{ab}{|ab|}\sqrt{a^2b^2+1}\\ b)\dfrac{\sqrt{ab+a}}{b^2}\\ c)\sqrt{a}\\ d)\dfrac{\sqrt{6}}{2}\\ e)-\sqrt{a}\\ f)\sqrt{p}\\ 3)\\ a)(\sqrt{x}+1)(y\sqrt{x}+1)\\ b)(x-y)(\sqrt{x}+\sqrt{y})$
Giải thích các bước giải:
$a)ab\sqrt{1+\dfrac{1}{a^2b^2}}\\ =ab\sqrt{\dfrac{a^2b^2}{a^2b^2}+\dfrac{1}{a^2b^2}}\\ =ab\sqrt{\dfrac{a^2b^2+1}{a^2b^2}}\\ =\dfrac{ab}{|ab|}\sqrt{a^2b^2+1}\\ b)\sqrt{\dfrac{a}{b^3}+\dfrac{a}{b^4}}\\ =\sqrt{\dfrac{ab}{b^4}+\dfrac{a}{b^4}}\\ =\sqrt{\dfrac{ab+a}{b^4}}\\ =\dfrac{\sqrt{ab+a}}{b^2}\\ c)\dfrac{a+\sqrt{ab}}{\sqrt{a}+\sqrt{b}}\\ =\dfrac{\sqrt{a}(\sqrt{a}+\sqrt{b})}{\sqrt{a}+\sqrt{b}}\\ =\sqrt{a}\\ d)\dfrac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}\\ =\dfrac{\sqrt{2}.\sqrt{2}.\sqrt{3}-\sqrt{6}}{\sqrt{2.4}-2}\\ =\dfrac{\sqrt{2}.\sqrt{6}-\sqrt{6}}{2\sqrt{2}-2}\\ =\dfrac{\sqrt{6}(\sqrt{2}-1)}{2(\sqrt{2}-1)}\\ =\dfrac{\sqrt{6}}{2}\\ e)\dfrac{a-\sqrt{a}}{1-\sqrt{a}}\\ =\dfrac{\sqrt{a}(\sqrt{a}-1)}{1-\sqrt{a}}\\ =-\sqrt{a}\\ f)\dfrac{p-2\sqrt{p}}{\sqrt{p}-2}\\ =\dfrac{\sqrt{p}(\sqrt{p}-2)}{\sqrt{p}-2}\\ =\sqrt{p}\\ 3)\\ a)xy+y\sqrt{x}+\sqrt{x}+1\\ =y\sqrt{x}(\sqrt{x}+1)+\sqrt{x}+1\\ =(\sqrt{x}+1)(y\sqrt{x}+1)\\ b)\sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}(ĐK: \ x \ge 0; y\ge 0)\\ =\sqrt{x^3}+\sqrt{x^2y}-\sqrt{y^3}-\sqrt{xy^2}\\ =x\sqrt{x}+x\sqrt{y}-y\sqrt{y}-y\sqrt{x}\\ =x(\sqrt{x}+\sqrt{y})-y(\sqrt{x}+\sqrt{y})\\ =(x-y)(\sqrt{x}+\sqrt{y})$
