Question

Найдите значение выражения √a²+12ab+36b² при a=8 1/5 и b= 4/5

Answer 1

$\sqrt{a^2+12ab+36b^2}=\sqrt{(a+6b)^2}=|a+6b|$

При  a = 8 1/5  и  b = 4/5

$\bigg|8\dfrac15+6\cdot\dfrac45\bigg|=\bigg|8\dfrac15+\dfrac{24}5\bigg|=\bigg|8\dfrac15+4\dfrac45\bigg|=\bigg|(8+4)+\bigg(\dfrac15+\dfrac45\bigg)\bigg|=\bigg|12+\dfrac55\bigg|=$

$=|12+1|=|13|=13$