مختبر تبسيط الجذور

التنفيذ

$\sqrt{99} = \sqrt{9 \times 11} = 3\sqrt{11}$

$\sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}$

$\sqrt{44} = \sqrt{4 \times 11} = 2\sqrt{11}$

$\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$

$E = -3(3\sqrt{11}) + 8(4\sqrt{2}) - 4(2\sqrt{11}) - 10(5\sqrt{2})$

$E = -9\sqrt{11} + 32\sqrt{2} - 8\sqrt{11} - 50\sqrt{2}$

التنفيذ

$f = \frac{\sqrt{2}-1}{\sqrt{2}+1} \times \frac{\sqrt{2}-1}{\sqrt{2}-1} = \frac{(\sqrt{2}-1)^2}{(\sqrt{2})^2 - 1^2} = \frac{2 - 2\sqrt{2} + 1}{2-1} = \frac{3-2\sqrt{2}}{1}$

التنفيذ

$e = \frac{2\sqrt{3}}{\sqrt{3}-4} \times \frac{\sqrt{3}+4}{\sqrt{3}+4} = \frac{2\sqrt{3}(\sqrt{3}+4)}{(\sqrt{3})^2 - 4^2} = \frac{2(3) + 8\sqrt{3}}{3-16} = \frac{6+8\sqrt{3}}{-13}$

التنفيذ

المقام المشترك = $(\sqrt{6})^2 - 2^2 = 6 - 4 = 2$.

$C = \frac{-\sqrt{6}(\sqrt{6}+2)}{2} + \frac{2(\sqrt{6}-2)}{2}$

$C = \frac{-6 - 2\sqrt{6} + 2\sqrt{6} - 4}{2}$

$C = \frac{-6 - 4}{2} = \frac{-10}{2}$

التنفيذ

المقام: $3\sqrt{20}-\sqrt{45} = 3\sqrt{4\times 5} - \sqrt{9\times 5} = 3(2\sqrt{5}) - 3\sqrt{5} = 6\sqrt{5}-3\sqrt{5} = 3\sqrt{5}$.

$A = 3\left(\frac{\sqrt{30}}{3\sqrt{5}}\right) = \frac{\sqrt{30}}{\sqrt{5}}$.

$A = \sqrt{\frac{30}{5}} = \sqrt{6}$.