Question

Лёгкая алгебра даю 70 баллов ​

Answer 1

Ответ:

$1)\ \ \sqrt{50}=\sqrt{2\cdot 25}=5\sqrt2 \ \ ;\qquad \sqrt{48}=\sqrt{3\cdot 16}=4\sqrt3\ \ ;\\\\\sqrt{160}=\sqrt{16\cdot 10}=4\sqrt{10}\ \ ;\qquad \sqrt{300}=\sqrt{3\cdot 100}=10\sqrt3\ \ ;\\\\\sqrt{108}=\sqrt{3\cdot 36}=6\sqrt3\ \ \ \ ;\ \ \ \ \ \ \ \sqrt{363}=\sqrt{3\cdot 121}=11\sqrt3\ \ ;\\\\\sqrt{375}=\sqrt{25\cdot 15}=5\sqrt{15}\ \ ;\ \qquad \sqrt{147}=\sqrt{49\cdot 3}=7\sqrt{3}\ \ .$

$2)\ \ \dfrac{1}{2}\sqrt{28}=\dfrac{1}{2}\sqrt{4\cdot 7}=\dfrac{1}{2}\cdot 2\sqrt7=\sqrt7\\\\-\dfrac{3}{5}\sqrt{500}=-\dfrac{3}{5}\sqrt{5\cdot 100}=-\dfrac{3}{5}\cdot 10\sqrt5=-6\sqrt5\\\\1,2\sqrt{75}=1,2\sqrt{25\cdot 3}=1,2\cdot 5\sqrt3=6\sqrt3\\\\-1,25\sqrt{48}=-1,25\sqrt{16\cdot 3}=-1,25\cdot 4\sqrt3=-5\sqrt3$

$3)\ \ 3\sqrt2=\sqrt{3^2\cdot 2}=\sqrt{18}\ \ ;\qquad 7\sqrt5=\sqrt{7^2\cdot 5}=\sqrt{49\cdot 5}=\sqrt{245}\ \ ;\\\\ -2\sqrt3=-\sqrt{2^2\cdot 3}=-\sqrt{12}\ \ ;\qquad -5\sqrt{10}=-\sqrt{5^2\cdot 10}=-\sqrt{250}\ \ ;\\\\10\sqrt{m}=\sqrt{10^2\cdot m}=\sqrt{100\, m}\ \ ;\qquad \dfrac{1}{2}\sqrt{8x}=\sqrt{\dfrac{1}{4}\cdot 8x}=\sqrt{2x}\ \ ;\\\\-0,1\sqrt{10a}=-\sqrt{0,01\cdot 10a}=-\sqrt{0,1a}\ \ ;\\\\7\sqrt{\dfrac{1}{7}c}=\sqrt{49\cdot \dfrac{1}{7}c}=\sqrt{7c}$