Question

найдите значение выражения

Answer 1

1)

$displaystyle sqrt{41^2-40^2}=sqrt{(41-40)*(41+40)}=sqrt{1*81}=9$

2)

$displaystyle sqrt{145^2-144^2}=sqrt{(145-144)(145-144)}=sqrt{1*289}=17$

3)

$displaystyle sqrt{8.5^5-7.5^2}=sqrt{(8.5-7.5)*(8.5+7.5)}=sqrt{1*16}=4$

4)

$displaystyle sqrt{21.8^2-18.2^2}=sqrt{(21.8-18.2)(21.8+18.2)}=sqrt{3.6*40}=sqrt{144}=12$

5)

$displaystyle sqrt{frac{155^2-134^2}{84}}=sqrt{frac{(155-134)(155+134)}{84}}=sqrt{frac{21*289}{84}} =sqrt{289/4}=\\=17/2=8.5$

6)

$displaystyle sqrt{frac{139^2-86^2}{98.5^2-45.5^2}}=sqrt{frac{(139-86)(139+86)}{(98.5-45.5)(98.5+45.5)}}=\\=sqrt{frac{53*225}{53*144}}=frac{15}{12} =1.25$