Question

Помогите пожалуйста с алгеброй за 8класс

Answer 1

1)

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

2)

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

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)

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