Решебник по алгебре 8 класс Мерзляк ФГОС Задание 538

 

\[\boxed{\mathbf{538\ (538).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \left( 2 - \sqrt{3} \right)\left( \sqrt{3} + 1 \right) =\]

\[= 2\sqrt{3} + 2 - 3 - \sqrt{3} = \sqrt{3} - 1;\]

\[2)\ \left( \sqrt{2} + \sqrt{5} \right)\left( 2\sqrt{2} - \sqrt{5} \right) =\]

\[= 2 \cdot 2 - \sqrt{10} + 2\sqrt{10} - 5 =\]

\[= \sqrt{10} - 1;\]

\[3)\ \left( a + \sqrt{b} \right)\left( a - \sqrt{b} \right) = a² - b;\]

\[4)\ \left( \sqrt{b} - \sqrt{c} \right)\left( \sqrt{b} + \sqrt{c} \right) = b - c;\]

\[5)\ \left( 4 + \sqrt{3} \right)\left( 4 - \sqrt{3} \right) = 16 - 3 =\]

\[= 13;\]

\[6)\ \left( y - \sqrt{7} \right)\left( y + \sqrt{7} \right) = y² - 7;\]

\[7)\ \left( 4\sqrt{2} - 2\sqrt{3} \right)\left( 2\sqrt{3} + 4\sqrt{2} \right) =\]

\[= \left( 4\sqrt{2} \right)^{2} - \left( 2\sqrt{3} \right)^{2} = 32 - 12 =\]

\[= 20;\]

\[8)\ \left( m + \sqrt{n} \right)^{2} = m² + 2m\sqrt{n} + n;\]

\[9)\ \left( \sqrt{a} - \sqrt{b} \right)^{2} = a - 2\sqrt{\text{ab}} + b;\]

\[10)\ \left( 2 - 3\sqrt{3} \right)^{2} =\]

\[= 4 - 12\sqrt{3} + 27 = 31 - 12\sqrt{3}.\]

\[\boxed{\mathbf{5}\mathbf{3}\mathbf{8}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \sqrt{m^{2}};\ \ если\ m > 0:\ \]

\[\sqrt{m^{2}} = |m| = m;\]

\[2)\ если\ n < 0:\ \ \]

\[\sqrt{n^{2}} = |n| = n;\]

\[3)\ если\ p \geq 0:\ \]

\[\sqrt{16p^{2}} = 4|p| = 4p;\]

\[4)\ если\ k \leq 0:\ \ \]

\[\sqrt{0,36k^{2}} = 0,6|k| = 0,6k;\]

\[5)\ \sqrt{c^{12}} = \left| c^{6} \right|;\]

\[6)\ если\ b \leq 0:\ \ \]

\[\sqrt{0,25b^{14}} = 0,5|b|^{7} = - 0,5b^{7};\]

\[7)\ если\ y \geq 0:\ \ \]

\[\sqrt{81x^{4}y^{2}} = 9x^{2}y;\]

\[8)\ если\ a \leq 0;\ \ b \geq 0:\]

\[\sqrt{0,01a^{6}b^{10}} = 0,1\left| a^{3} \right|\left| b^{5} \right| =\]

\[= - 0,1a^{3}b^{5};\]

\[9)\ если\ x \leq 0:\]

\[- 1,2x\sqrt{64x^{18}} =\]

\[= - 1,2x \cdot 8 \cdot \left| x^{9} \right| = 96x^{10};\]

\[10)\ если\ b < 0:\ \]

\[\frac{\sqrt{a^{12} \cdot b^{22} \cdot c^{36}}}{a^{4} \cdot b^{8} \cdot c^{10}} = \frac{\left| a^{6} \right|\left| b^{11} \right|\left| c^{18} \right|}{a^{4} \cdot b^{8} \cdot c^{10}} =\]

\[= \frac{- a^{6} \cdot b^{11} \cdot c^{18}}{a^{4} \cdot b^{8} \cdot c^{10}} = - a^{2} \cdot b^{3} \cdot c^{8};\]

\[11)\ если\ a < 0:\]

\[\frac{3,3a^{4}}{b^{3}} \cdot \sqrt{\frac{b^{24}}{121a^{26}}} = \frac{3,3a^{4}\left| b^{12} \right|}{b^{3} \cdot 11\left| a^{13} \right|} =\]

\[= \frac{- 0,3b^{9}}{a^{9}} = - \frac{3b^{9}}{10a^{9}};\]

\[12)\ если\ m \leq 0:\]

\[- 0,5m^{5} \cdot \sqrt{1,96m^{6}n^{8}} =\]

\[= - 0,5m^{5} \cdot 1,4\left| m^{3} \right|n^{4} =\]

\[= 0,7m^{8}n^{4}\text{.\ }\]