Question

ПОЖАЛУЙСТААА ПОМОГИТЕ  

 

а) $sqrt{36} + 10sqrt{11} + sqrt{47 - 12 sqrt{11}}$

 

 

б) $sqrt{87} - 16sqrt{23} - sqrt{39 - 8 sqrt{23}}$

 

 

Answer 1

$sqrt{36+10sqrt{11}}+sqrt{47-12sqrt{11}}=\ sqrt{25+10sqrt{11}+11}+sqrt{36-12sqrt{11}+11}=\ sqrt{5^2+2*5sqrt{11}+(sqrt{11})^2}+sqrt{6^2-2*6sqrt{11}+(sqrt{11})^2}=\ sqrt{(5+sqrt{11})^2}+sqrt{(6-sqrt{11})^2}=\ |5+sqrt{11}|+|6-sqrt{11}|=\ 5+sqrt{11}+6-sqrt{11}=5+6=11$

 

$sqrt{87-16sqrt{23}}-sqrt{39-8sqrt{23}}=\ sqrt{64-16sqrt{23}+23}-sqrt{16-8sqrt{23}+23}=\ sqrt{8^2-2*8sqrt{23}+(sqrt{23})^2}-sqrt{4^2-2*4sqrt{23}+(sqrt{23})^2}=\ sqrt{(8-sqrt{23})^2}-sqrt{(4-sqrt{23})^2}=\ |8-sqrt{23}|-|4-sqrt{23}|=\ (8-sqrt{23})-(sqrt{23}-4)=8-sqrt{23})^2-sqrt{23}+4=8+4=12$