تدرب وحل التمرينات

بسط الجمل العددية التالية باستعمال الخواص (الأبدال، التجميع، التوزيع):

$\sqrt{2}(1+7\sqrt{2})$

$\sqrt{2}+7\times 2=\sqrt{2}+14$

$\sqrt{5}(\sqrt{20}-\sqrt{5})$

$\sqrt{100}-\sqrt{25}=10-5=5$

$4\sqrt{18}-6\sqrt{32}$

$12\sqrt{2}-24\sqrt{2}=-12\sqrt{2}$

$\sqrt{10}(3\sqrt{5}-7\sqrt{2})$

$3\sqrt{50}-7\sqrt{20}=15\sqrt{5}-14\sqrt{5}=\sqrt{5}$

$\sqrt{54}(2-\sqrt{2})$

$2\sqrt{54}-\sqrt{108}=6\sqrt{6}-6\sqrt{3}$

$\sqrt{7}(\sqrt{14}-5\sqrt{7})$

$\sqrt{98}-35=7\sqrt{2}-35$

بسط الجمل العددية التالية باستعمال الخواص (العنصر المحايد، النظير الجمعي والنظير الضربي):

$\frac{9-2\sqrt{5}}{3\sqrt{5}}$

$\frac{9-2\sqrt{5}}{3\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}=\frac{9\sqrt{5}-10}{15}$

$\frac{\sqrt{6}-5}{\sqrt{3}\sqrt{2}}$

$\frac{\sqrt{6}-5}{\sqrt{3}\sqrt{2}}\times \frac{\sqrt{3}\sqrt{2}}{\sqrt{3}\sqrt{2}}=\frac{6-5\sqrt{6}}{6}$

$\frac{\sqrt{75}-\sqrt{36}}{2\sqrt{12}}$

$\frac{5\sqrt{3}-6}{4\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=\frac{5-2\sqrt{3}}{4}$

$\frac{\sqrt{40}-\sqrt{2}}{\sqrt{5}}$

$\frac{2\sqrt{10}-\sqrt{2}}{\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}=\frac{10\sqrt{2}-\sqrt{10}}{5}$

بسط الجمل العددية التالية باستعمال خصائص الأعداد الحقيقية:

$\sqrt{2}(7+\sqrt{3})-4\sqrt{6}$

$7\sqrt{2}+\sqrt{6}-4\sqrt{6}=7\sqrt{2}-3\sqrt{6}$

$\sqrt{5}(\sqrt{5}+\sqrt{50})-8\sqrt{2}$

$5+5\sqrt{10}-8\sqrt{2}$

$3\sqrt{8}+3(\sqrt{6}-\sqrt{72})$

$6\sqrt{2}+3\sqrt{6}-9\sqrt{8}$

$\frac{1}{6}\sqrt{13}+\frac{1}{2}(\sqrt{52}-\frac{1}{3}\sqrt{13})$

$\frac{1}{6}\sqrt{13}+\sqrt{13}-\frac{1}{6}\sqrt{13}=\sqrt{13}$

$\frac{8\sqrt{6}}{\sqrt{8}}÷\frac{12\sqrt{3}}{\sqrt{98}}$

$\frac{8\sqrt{2}\sqrt{3}}{2\sqrt{2}}\times \frac{7\sqrt{2}}{12\sqrt{3}}=\frac{7}{3}\sqrt{2}$

$\frac{9\sqrt{1}}{\sqrt{15}}\times \frac{10\sqrt{12}}{\sqrt{18}}$

$\frac{9}{\sqrt{3}\sqrt{5}}\times \frac{20\sqrt{3}}{3\sqrt{2}}=\frac{60}{\sqrt{10}}\times \frac{\sqrt{10}}{\sqrt{10}}=\frac{6\sqrt{10}}{10}$