Решебник по алгебре 8 класс Мерзляк Задание 508

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\[1)\ \sqrt{41^{2} - 40^{2}} =\]

\[= \sqrt{(41 - 40)(41 + 40)} =\]

\[= \sqrt{1 \cdot 81} = 9\]

\[2)\ \sqrt{145^{2} - 144^{2}} =\]

\[= \sqrt{(145 - 144)(145 + 144)} =\]

\[= \sqrt{1 \cdot 289} = 17\]

\[3)\ \sqrt{{8,5}^{2} - {7,5}^{2}} =\]

\[= \sqrt{(8,5 - 7,5)(8,5 + 7,5)} =\]

\[= \sqrt{1 \cdot 16} = 4\]

\[4)\ \sqrt{{21,8}^{2} - {18,2}^{2}} =\]

\[= \sqrt{(21,8 - 18,2)(21,8 + 18,2)} =\]

\[= \sqrt{3,6 \cdot 40} =\]

\[= \sqrt{36 \cdot 4} = 6 \cdot 2 = 12\]

\[5)\ \sqrt{\frac{155^{2} - 134^{2}}{84}} =\]

\[= \sqrt{\frac{(155 - 134)(155 + 134)}{84}} =\]

\[= \sqrt{\frac{21 \cdot 289}{84}} = \sqrt{\frac{289}{4}} =\]

\[= \frac{17}{2} = 8,5\]

\[6)\ \sqrt{\frac{139^{2} - 86^{2}}{{98,5}^{2} - {45,5}^{2}}} =\]

\[= \sqrt{\frac{(139 - 86)(139 + 86)}{(98,5 - 45,5)(98,5 + 45,5)}} =\]

\[= \sqrt{\frac{53 \cdot 225}{53 \cdot 144}} = \frac{15}{12} = \frac{5}{4} = 1\frac{1}{4}\]