Реши задание на изображении
Краткий ответ
320.
а) \(x\ge 0\);
б) \(x\le 0\).
321.
\[
25;\ 81;\ 2;\ 3;\ 4;\ 5;\ 6;\ \frac12;\ 1{,}3.
\]
322.
а) \(7\); б) \(26\); в) \(-28\); г) \(45\); д) \(4\); е) \(60\); ж) \(\frac34\); з) \(\frac12\).
Решение
320
Квадратный корень имеет смысл, если подкоренное выражение неотрицательно:
а)
\[
2x\ge0 \quad\Rightarrow\quad x\ge0.
\]
б)
\[
-x\ge0 \quad\Rightarrow\quad x\le0.
\]
321
Используем правило: \[ (\sqrt a)^2=a,\qquad (-\sqrt a)^2=a. \]
Поэтому: \[ (\sqrt{25})^2=25,\quad (\sqrt{81})^2=81,\quad (\sqrt2)^2=2,\quad (\sqrt3)^2=3; \]
\[ (-\sqrt4)^2=4,\quad (\sqrt5)^2=5,\quad (-\sqrt6)^2=6; \]
\[ \left(\sqrt{\frac12}\right)^2=\frac12,\qquad (\sqrt{1{,}3})^2=1{,}3. \]
322
а)
\[
(\sqrt7)^2=7.
\]
б)
\[
(-\sqrt{26})^2=26.
\]
в)
\[
-2\sqrt{14}\cdot\sqrt{14}
=-2\cdot14=-28.
\]
г)
\[
(3\sqrt5)^2=3^2\cdot(\sqrt5)^2=9\cdot5=45.
\]
д)
\[
0{,}5(-\sqrt8)^2=0{,}5\cdot8=4.
\]
е)
\[
(-2\sqrt{15})^2=(-2)^2\cdot(\sqrt{15})^2
=4\cdot15=60.
\]
ж)
\[
\left(\frac{\sqrt3}{2}\right)^2
=\frac{(\sqrt3)^2}{2^2}
=\frac34.
\]
з)
\[
\left(\frac{\sqrt3}{\sqrt6}\right)^2
=\frac{3}{6}=\frac12.
\]
Проверка: результаты выражений с квадратом неотрицательны, кроме пункта в), где перед произведением стоит знак «минус».
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