شاه کلید نکات
شاه کلید سوال
1 تساوی ها را کامل کنید.
\(\begin{array}{l}\sqrt {16} = \\\\ - \sqrt {16} = \\\\\sqrt {36} = \\\\ - \sqrt {81} = \\\\\sqrt {\frac{1}{{100}}} = \\\\ - \sqrt {\frac{9}{{25}}} = \\\\\sqrt {49} = \\\\\sqrt {\frac{1}{{81}}} = \end{array}\)
\(\begin{array}{l}\sqrt {16} = 4\\\\ - \sqrt {16} = - 4\\\\\sqrt {36} = 6\\\\ - \sqrt {81} = - 9\\\\\sqrt {\frac{1}{{100}}} = \frac{1}{{10}}\\\\ - \sqrt {\frac{9}{{25}}} = - \frac{3}{5}\\\\\sqrt {49} = 7\\\\\sqrt {\frac{1}{{81}}} = \frac{1}{9}\end{array}\)
2 کدام یک درست و کدام یک نادرست است؟ علت نادرستی را توضیح دهید.
\(\begin{array}{l}\sqrt {25} > 5\\\\\sqrt {25} = 5\\\\\sqrt {25} = 5 \times 2\\\\\sqrt {25} = {2^5}\\\\\sqrt {25} = {5^2}\\\\\sqrt {25} = - 5\\\\ - \sqrt {25} = - 5\\\\\sqrt {25} < 5\end{array}\)
\(\sqrt {25} > 5\)
نادرست است؛ زیرا:
\(\sqrt {25} = 5\)
\(\sqrt {25} = 5\)
درست می باشد.
\(\sqrt {25} = 5 \times 2\)
نادرست است؛ زیرا:
\(\begin{array}{l}\left\{ \begin{array}{l}\sqrt {25} = 5\\\\5 \times 2 = 10\end{array} \right.\\\\ \Rightarrow \sqrt {25} \ne 5 \times 2\end{array}\)
\(\sqrt {25} = {2^5}\)
نادرست است؛ زیرا:
\(\begin{array}{l}\left\{ \begin{array}{l}\sqrt {25} = 5\\\\{2^5} = 32\end{array} \right.\\\\ \Rightarrow \sqrt {25} \ne {2^5}\end{array}\)
\(\sqrt {25} = {5^2}\)
نادرست است؛ زیرا:
\(\begin{array}{l}\left\{ \begin{array}{l}\sqrt {25} = 5\\\\{5^2} = 25\end{array} \right.\\\\ \Rightarrow \sqrt {25} \ne {5^2}\end{array}\)
\(\sqrt {25} = - 5\)
نادرست است؛ زیرا:
\(\sqrt {25} = 5 \ne - 5\)
\( - \sqrt {25} = - 5\)
درست می باشد؛ زیرا:
\(\begin{array}{l}\sqrt {25} = 5\\\\ \Rightarrow - \sqrt {25} = - 5\end{array}\)
\(\sqrt {25} < 5\)
نادرست است؛ زیرا:
\(\sqrt {25} = 5\)
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