[2-2] خصائص الأعداد الحقيقية

اختر الإجابة الصحيحة لكل مما يأتي:

اكتب مثالاً لكل خاصية من الخواص الآتية:

$\begin{array}{rl}& \mathrm{a}+(-\mathrm{a})=0,\mathrm{\forall }\mathrm{a},-\mathrm{a}\in \mathrm{R}\end{array}$

• $\begin{array}{rl}& \frac{5}{\sqrt{7}}+\frac{\sqrt{7}}{5}=0\end{array}$
• $\begin{array}{rl}& \frac{\mathbf{5}}{\sqrt{\mathbf{7}}}\mathbf{+}\mathbf{(}\mathbf{-}\frac{\mathbf{5}}{\sqrt{\mathbf{7}}}\mathbf{)}\mathbf{=}\mathbf{0}\end{array}$
• $\begin{array}{rl}& \frac{5}{\sqrt{7}}+\frac{5}{\sqrt{7}}=0\end{array}$
• $\begin{array}{rl}& \frac{5}{\sqrt{7}}+(-\frac{\sqrt{7}}{5})=0\end{array}$

$\begin{array}{rl}& a\times \frac{1}{a}=1,\mathrm{\forall }a\in R,a\ne 0\end{array}$

• $\begin{array}{rl}& \frac{1}{\sqrt{3}}\times \frac{1}{\sqrt{3}}=1\end{array}$
• $\begin{array}{rl}& \frac{1}{\sqrt{3}}\times \frac{-1}{\sqrt{3}}=1\end{array}$
• $\begin{array}{rl}& \frac{\mathbf{1}}{\sqrt{\mathbf{3}}}\mathbf{\times }\sqrt{\mathbf{3}}\mathbf{=}\mathbf{1}\end{array}$
• $\begin{array}{rl}& \frac{1}{\sqrt{3}}\times (-\sqrt{3})=1\end{array}$

جد النظير الجمعي للأعداد الحقيقية الآتية:

$\begin{array}{rl}& 7\sqrt{5}-8\end{array}$

• $\begin{array}{rl}& 7\sqrt{5}+8\end{array}$
• $\begin{array}{rl}& -7\sqrt{5}-8\end{array}$
• $\begin{array}{rl}& \frac{1}{7\sqrt{5}-8}\end{array}$
• $\mathbf{-}\mathbf{7}\sqrt{\mathbf{5}}\mathbf{+}\mathbf{8}$

$\begin{array}{rl}& -\sqrt{1}-\sqrt{2}\end{array}$

• $\begin{array}{rl}& \mathbf{1}\mathbf{+}\sqrt{\mathbf{2}}\end{array}$
• $\begin{array}{rl}& \sqrt{1}-\sqrt{2}\end{array}$
• $\begin{array}{rl}& \sqrt{2}-\sqrt{1}\end{array}$
• $-1-\sqrt{2}$

$\begin{array}{rl}& \frac{2}{\sqrt{11}}-\frac{6}{\sqrt{11}}\end{array}$

• $\begin{array}{rl}& \frac{-8}{\sqrt{11}}\end{array}$
• $\begin{array}{rl}& \frac{-4}{\sqrt{11}}\end{array}$
• $\begin{array}{rl}& \frac{\mathbf{4}}{\sqrt{\mathbf{11}}}\end{array}$
• $\frac{\sqrt{11}}{4}$

جد النظير الضربي للأعداد الحقيقية الآتية:

$\begin{array}{rl}& -\sqrt{\frac{1}{12}}\end{array}$

• $2\sqrt{3}$
• $\begin{array}{rl}& \frac{-1}{2\sqrt{3}}\end{array}$
• $\mathbf{-}\mathbf{2}\sqrt{\mathbf{3}}$
• $\begin{array}{rl}& \frac{1}{2\sqrt{3}}\end{array}$

$\begin{array}{rl}& \sqrt{7}-\frac{1}{\sqrt{7}}\end{array}$

• $\frac{-6}{\sqrt{7}}$
• $\begin{array}{rl}& \frac{\sqrt{\mathbf{7}}}{\mathbf{6}}\end{array}$
• $\frac{6}{\sqrt{7}}$
• $\begin{array}{rl}& \frac{\sqrt{7}}{8}\end{array}$

$\begin{array}{rl}& -6\frac{2}{5}-3\frac{3}{5}\end{array}$

• $\frac{5}{14}$
• $\frac{-5}{14}$
• $\frac{1}{10}$
• $\frac{\mathbf{-}\mathbf{1}}{\mathbf{10}}$

قدر النظير الضربي للجذور التربيعية التالية بالتقريب لأقرب عشر:

$\sqrt{\frac{1}{7}}$

• $\frac{1}{2.6}$
• 2.6
• $\begin{array}{rl}& \frac{-1}{2.6}\end{array}$
• 2.6-

$-\sqrt{\frac{11}{25}}$

• $\frac{2}{3.3}$
• $\frac{3.3}{5}$
• $\begin{array}{rl}& \frac{\mathbf{-}\mathbf{5}}{\mathbf{3}\mathbf{.3}}\end{array}$
• $\frac{-3.3}{5}$