Question

Решите без калькулятора обычным школьным методом пожалуйста.​

Answer 1

286

$\displaystyle \sqrt{21*6*7*8}=\sqrt{3*7*2*3*7*2*4}=\sqrt{3^2*7^2*2^2*4}=3*7*2*2= 84 \\\\\sqrt{72*6*45*15}=\sqrt{(2*4*9)*(2*3)*(5*9)*(5*3)}=\sqrt{9^2*5^2*3^2*2^2*4}=\\\\=9*5*3*2*2= 540 \\\\\sqrt{225*0.16*400}=\sqrt{\frac{25*9*4*4*4*100}{100}}=\frac{5*3*2*2*2*10}{10}=120\\\\\sqrt{900*25*1.69}=\sqrt{\frac{9*100*25*169}{100}}=\frac{3*10*5*13}{10}= 195$

287

$\displaystyle \sqrt{7}*\sqrt{63}=\sqrt{7*7*9}=7*3=21\\\\\sqrt{8}*\sqrt{98}=\sqrt{2*4*2*49}=2*2*7=28\\\\\sqrt{75}*\sqrt{3}=\sqrt{25*3*3}=5*3=15\\\\\sqrt{10}*\sqrt{40}=\sqrt{10*4*10}=2*10=20\\\\\sqrt{30*270}=\sqrt{3*10*3*9*10}=3*3*10=90\\\\\sqrt{11*44}=\sqrt{11*4*11}=11*2=22$