Đáp án:
$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 1:\\ a.\ 300\\ b.\ 18|b|\sqrt{a}\\ c.\ 90a^{2}\sqrt{b}\\ Bài\ 2:\\ a.\sqrt{98}\\ b.\sqrt{3x}\\ c.\ \sqrt{x^{4} y}\\ d.\sqrt{3a^{2} -6ab+3b^{2}}\\ e.\ \sqrt{2( a-b)}\\ Bài\ 3:\\ a.\ 4\sqrt{2}\\ b.\ 24\sqrt{14} +336\\ c.12 \end{array}$
Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} Bài\ 1:\\ a.\ =\sqrt{5.5^{2} .2.6^{2} .10} =5.6.10=300\\ b.\ =\sqrt{( -3)^{2}( -6)^{2} .ab^{2}} =( -3) .( -6) |b|\sqrt{a} =18|b|\sqrt{a}\\ c.\ =\sqrt{3.5^{2} .3^{3} .2^{2} a^{4} b} =5.9.2.a^{2}\sqrt{b} =90a^{2}\sqrt{b}\\ Bài\ 2:\\ a.=\sqrt{( -7)^{2} .2} =\sqrt{98}\\ b.=\sqrt{( -x)^{2} .\frac{3}{x}} =\sqrt{x^{2} .\frac{3}{x}} =\sqrt{3x}\\ c.=\ \sqrt{x^{4} y}\\ d.=\ \sqrt{3( a-b)^{2}} =\sqrt{3a^{2} -6ab+3b^{2}}\\ e.\ =\sqrt{\frac{2}{a-b}[ -( a-b)]^{2}} =\sqrt{\frac{2}{a-b}( a-b)^{2}} =\sqrt{2( a-b)}\\ Bài\ 3:\\ a.\ 2\sqrt{2} -4\sqrt{2} +6\sqrt{2} =4\sqrt{2}\\ b.\ \left( 6\sqrt{2} -3\sqrt{7} +15\sqrt{7}\right) 4\sqrt{7} =\ \left( 6\sqrt{2} +12\sqrt{7}\right) 4\sqrt{7} =24\sqrt{14} +336\\ c.\ \left( 40\sqrt{3} -18\sqrt{3} +2\sqrt{3}\right) :2\sqrt{3} =24\sqrt{3} :2\sqrt{3} =12 \end{array}$
