ГДЗ по алгебре 8 класс Макарычев Задание 493

\[\boxed{\text{493\ (493).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\mathbf{Вспомним:}\]

\[\sqrt{\mathbf{a}}\mathbf{\cdot}\sqrt{\mathbf{b}}\mathbf{=}\sqrt{\mathbf{\text{ab}}}\mathbf{;\ \ }\]

\[\mathbf{при\ }\mathbf{a \geq 0;\ \ b \geq 0.}\]

Решение.

\[\textbf{а)}\ \sqrt{x}(\sqrt{a} - \sqrt{b}) = \sqrt{\text{ax}} - \sqrt{\text{bx}}\]

\[\textbf{б)}\ \left( \sqrt{x} + \sqrt{y} \right)\sqrt{x} = \sqrt{x^{2}} + \sqrt{\text{xy}} =\]

\[= x + \sqrt{\text{xy}}\]

\[\textbf{в)}\ \sqrt{\text{ab}}\left( \sqrt{a} + \sqrt{b} \right) =\]

\[= \sqrt{a^{2}b} + \sqrt{ab^{2}} = a\sqrt{b} + b\sqrt{a}\ \]

\[\textbf{г)}\ \left( \sqrt{m} - \sqrt{n} \right)\sqrt{\text{mn}} =\]

\[= \sqrt{m^{2}n} - \sqrt{mn^{2}} = m\sqrt{n} - n\sqrt{m}\]

\[\textbf{д)}\ \left( \sqrt{x} + \sqrt{y} \right)\left( 2\sqrt{x} - \sqrt{y} \right) =\]

\[= 2x + \sqrt{\text{xy}} - y\]

\[\textbf{е)}\ \left( \sqrt{a} - \sqrt{b} \right)\left( 3\sqrt{a} + 2\sqrt{b} \right) =\]

\[= 3a - \sqrt{\text{ab}} - 2b\]

\[\textbf{ж)}\ \left( 2\sqrt{a} + \sqrt{b} \right)\left( 3\sqrt{a} - 2\sqrt{b} \right) =\]

\[= 6a - \sqrt{\text{ab}} - 2b\]

\[\textbf{з)}\ \left( 4\sqrt{x} - \sqrt{2x} \right)\left( \sqrt{x} - \sqrt{2x} \right) =\]

\[= 4x - 5x\sqrt{2} + 2x = 6x - 5x\sqrt{2}\ \]