Răspuns:
Explicație pas cu pas:
a)√200=√10²·2=10√2 adevarata
b)-√343=-√7³=-7√7 falsa cea din text
c) √a²b=IaI√b=a√b adverata a>0 si b>0
d) √ab²=IbI√a=-b√a adevarata b<0 si a>0
e)√288=√2·144=12√2=12√x x=2 adevarata
f)√675=√3³·5²=5·3√3=x√3 ⇒x=15 falsa
[tex]\it a)\ \sqrt{200}=\sqrt{100\cdot2}=10\sqrt2\ \ (A)\\ \\ b)\ -\sqrt{343}=7\sqrt7\ \ (F),\ \ -\sqrt{343}<0,\ \ 7\sqrt7>0\\ \\ -\sqrt{343}=-\sqrt{49\cdot7}=-7\sqrt7\ \ (A)\\ \\ c)\ \sqrt{a^2\cdot b}=|a|\sqrt b=a\sqrt b,\ \ pentru\ \ a>0\ \ \ (A)\\ \\ d)\ \sqrt{a\cdot b^2}=|b|\sqrt a=-b\sqrt a,\ \ pentru\ \ b<0\ \ \ (A)\\ \\ e)\ \sqrt{288}=12\sqrt x \Rightarrow \sqrt{144\cdot2}=12\sqrt x \Rightarrow 12\sqrt2=12\sqrt x \Rightarrow x=2\ \ \ (A)[/tex]
[tex]\it f)\ \sqrt{675}=x\sqrt3 \Rightarrow \sqrt{225\cdot3}=x\sqrt3 \Rightarrow 15\sqrt3=x\sqrt5 \Rightarrow x=15\ \ \ \ (A)\\ \\ (Propozi\c{\it t}ia\ din\ enun\c{\it t}\ este\ fals\breve a)[/tex]
