Question

Помогите пожалуйста с алгеброй за 8класс

Answer 1

1)

$\frac{15+2\sqrt{26}}{\sqrt{13}+\sqrt{2}} = \frac{13+2\sqrt{2*13}+2}{\sqrt{13}+\sqrt{2}} = \frac{(\sqrt{13}+\sqrt{2})^2}{\sqrt{13}+\sqrt{2}} = \sqrt{13}+\sqrt{2}$

2)

$\frac{14-2\sqrt{33}}{\sqrt{11}-\sqrt{3}} = \frac{11-2\sqrt{11*3}+3}{\sqrt{11}-\sqrt{3}} =\frac{(\sqrt{11})^2-2\sqrt{11}*\sqrt{3} +(\sqrt{3})^2}{\sqrt{11}-\sqrt{3}} = \frac{(\sqrt{11}-\sqrt{3})^2}{\sqrt{11}-\sqrt{3}} = \sqrt{11}-\sqrt{3}$

3)

$\frac{\sqrt{30}+\sqrt{6}-\sqrt{5}-1}{\sqrt{5}+1} = \frac{(\sqrt{30}+\sqrt{6})-(\sqrt{5}+1)}{\sqrt{5}+1} = \frac{(\sqrt{6*5}+\sqrt{6})-(\sqrt{5}+1)}{\sqrt{5}+1} = \frac{\sqrt{6} (\sqrt{5}+1)-(\sqrt{5}+1)}{\sqrt{5}+1} = \frac{(\sqrt{6}-1)*(\sqrt{5}+1)}{\sqrt{5}+1} = \sqrt{6}-1$

4)

$\frac{\sqrt{14}+\sqrt{7}-2\sqrt{2}-2}{\sqrt{7}-2} = \frac{(\sqrt{14}+\sqrt{7})-(2\sqrt{2}+2)}{\sqrt{7}-2} = \frac{(\sqrt{7*2}+\sqrt{7})-(2\sqrt{2}+2)}{\sqrt{7} -2} = \frac{\sqrt{7} (\sqrt{2}+1)-2*(\sqrt{2}+1)}{\sqrt{7}-2} = \frac{(\sqrt{2}+1)*(\sqrt{7}-2)}{\sqrt{7}-2} = \sqrt{2}+1$