[2-3] تبسيط الجمل العددية التي تحتوي على جذور تربيعية

اختر الإجابة الصحيحة لكل مما يأتي:

بسط الجمل العددية التالية باستعمال خصائص الأعداد الحقيقية:

$\begin{array}{rl}& \sqrt{3}(\sqrt{12}-\sqrt{2})\end{array}$

• $6-3\sqrt{2}$
• $6+3\sqrt{2}$
• $6+\sqrt{6}$
• $\mathbf{6}\mathbf{-}\sqrt{\mathbf{6}}$

$\begin{array}{rl}& 7\sqrt{20}-3\sqrt{45}\end{array}$

• $23\sqrt{5}$
• $\mathbf{5}\sqrt{\mathbf{5}}$
• $-23\sqrt{5}$
• $-5\sqrt{5}$

$\begin{array}{rl}& \sqrt{32}(2^3-\sqrt{8})\end{array}$

• $16-32\sqrt{2}$
• $32\sqrt{2}+16$
• $\mathbf{32}\sqrt{\mathbf{2}}\mathbf{-}\mathbf{16}$
• $32-16\sqrt{2}$

$\begin{array}{rl}& \sqrt{5}(3+\sqrt{10})-5\sqrt{2}\end{array}$

• $\mathbf{3}\sqrt{\mathbf{5}}$
• $-5\sqrt{5}$
• $3\sqrt{2}$
• $-5\sqrt{2}$

$\begin{array}{rl}& \sqrt[3]{-27}(\sqrt{7}+1^3)+7\sqrt{7}\end{array}$

• $4\sqrt{7}-9$
• $10\sqrt{7}-3$
• $10\sqrt{7}-9$
• $\mathbf{4}\sqrt{\mathbf{7}}\mathbf{-}\mathbf{3}$

$\begin{array}{rl}& \frac{1}{9}\sqrt{11}+\frac{1}{6}(\sqrt{11}-\frac{1}{3}\sqrt{11})\end{array}$

• $\frac{-\sqrt{11}}{6}$
• $\frac{2}{9}\sqrt{11}$
• $\frac{3\sqrt{11}}{-6}$
• $\frac{\mathbf{7}\sqrt{\mathbf{11}}}{\mathbf{-}\mathbf{6}}$

$\begin{array}{rl}& \frac{1-5\sqrt{3}}{4\sqrt{3}}\end{array}$

• $\frac{\sqrt{\mathbf{3}}\mathbf{-}\mathbf{15}}{\mathbf{12}}$
• $\frac{\sqrt{3}+15}{12}$
• $\frac{\sqrt{3}-5}{4}$
• $\frac{\sqrt{3}+5}{4}$

بسط الجمل العددية التالية باستعمال خاصية تنسيب المقام:

$\begin{array}{rl}& \frac{\sqrt{8}-\sqrt{28}}{\sqrt{7}\sqrt{2}}\end{array}$

• $\begin{array}{rl}& \frac{\mathbf{2}\sqrt{\mathbf{7}}\mathbf{-}\mathbf{7}\sqrt{\mathbf{2}}}{\mathbf{7}}\end{array}$
• $\begin{array}{rl}& \frac{2\sqrt{7}+7\sqrt{2}}{7}\end{array}$
• $\begin{array}{rl}& \frac{2\sqrt{7}-7\sqrt{2}}{14}\end{array}$
• $\begin{array}{rl}& \frac{2\sqrt{7}+7\sqrt{2}}{14}\end{array}$

$\begin{array}{rl}& \frac{\sqrt{98}-\sqrt{18}}{3\sqrt{24}}\end{array}$

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

$\begin{array}{rl}& \frac{10\sqrt{6}}{\sqrt{48}}÷\frac{5\sqrt{2}}{\sqrt{49}}\end{array}$

• $\frac{2}{7}$
• $-\frac{7}{2}$
• $\frac{\mathbf{7}}{\mathbf{2}}$
• $-\frac{2}{7}$

$\begin{array}{rl}& \frac{20\sqrt{1}}{\sqrt[3]{-54}}\times \frac{\sqrt[3]{-16}}{\sqrt{20}}\end{array}$

• $\frac{\mathbf{20}}{\mathbf{3}\sqrt{\mathbf{5}}}$
• $\frac{40}{3\sqrt{5}}$
• $\frac{-20}{3\sqrt{5}}$
• $\frac{-40}{3\sqrt{5}}$