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信息发布者：
因式分解
​$ D$​
$4\sqrt{3}$
$10\sqrt{5}$
解：​$\sqrt {6} × \sqrt {60} $​
​$= \sqrt {6×60} $​
​$= \sqrt {360} $​
​$= \sqrt {36×10}$​
​$= 6\sqrt {10}$​
解：​$2\sqrt {5} × 3\sqrt {15} $​
​$= (2×3)×\sqrt {5×15} $​
​$= 6×\sqrt {75} $​
​$= 6×5\sqrt {3} $​
​$= 30\sqrt {3}$​
解：​$\sqrt {144} × 3\sqrt {\frac {1}{8}}$​
​$ = 12 × 3×\sqrt {\frac {1}{8}} $​
​$= 36×\frac {\sqrt {2}}{4} $​
​$= 9\sqrt {2}$​
解：​$3\sqrt {6} × 4\sqrt {\frac {9}{2}} $​
​$= (3×4)×\sqrt {6×\frac {9}{2}} $​
​$= 12×\sqrt {27} $​
​$= 12×3\sqrt {3}$​
​$ = 36\sqrt {3}$​
解：​$4\sqrt {xy} × \sqrt {\frac {1}{y}} $​
​$= 4×\sqrt {xy×\frac {1}{y}}$​
​$ = 4\sqrt {x}$​
解：​$3\sqrt {5a} × 2\sqrt {10b} $​
​$= (3×2)×\sqrt {5a×10b} $​
​$= 6×\sqrt {50ab} $​
​$= 6×5\sqrt {2ab}$​
​$ = 30\sqrt {2ab}$​
解：∵​$0＜x＜y，$​
∴​$x-y＜0$​
​$ \sqrt {(x+2y)^2(x-y)^2} $​
​$= |x+2y|·|x-y| $​
​$= (x+2y)(y-x)$​
解：​$\sqrt {125y^2z^3 × 25y^3z^2} $​
​$= \sqrt {125×25× y^5z^5} $​
​$= \sqrt {3125y^5z^5}$​
​$ = 25y^2z^2\sqrt {5yz}$​
解：​$\sqrt {a^5+2a^3b^2+ab^4}$​
​$ = \sqrt {a(a^4+2a^2b^2+b^4)}$​
​$ = \sqrt {a(a^2+b^2)^2}$​
​$ = (a^2+b^2)\sqrt {a}$​
解：​$\sqrt {16a^3+32a^2} $​
​$= \sqrt {16a^2(a+2)} $​
​$= 4a\sqrt {a+2}$​
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