Question

Решите примеры с корнями, даю 20 балов

Answer 1

$1)\ \ \sqrt{49}=7\ \ ;\ \ \sqrt{0,25}=0,5\ \ ;\ \ \sqrt{\dfrac{4}{289}}=\dfrac{2}{17}\ \ ;\ \ \sqrt{1\dfrac{15}{49}}=\sqrt{\dfrac{64}{49}}=\dfrac{8}{7}$

$2)\ \ a)\ \ \ \sqrt{3x}\ \ \to \ \ \ x\geq 0\\\\{}\ \ \ b)\ \ \ \sqrt{-7x}\ \ \to \ \ \ x\leq 0\\\\{}\ \ \ c)\ \ \ \dfrac{4x}{\sqrt{x}}\ \ \ \ \ \to \ \ \ x>0\\\\{}\ \ \ d)\ \ \ \dfrac{19}{\sqrt{x}-6}\ \ \to \ \ \ \sqrt{x}-6\ne 0\ \ i\ \ x\geq 0\ \ \to \ \ \ x\ne 36\ \ i\ \ x\geq 0,\\\\{}\ \ \ x\in (\ 0\ ;\, 36\, )\cup (\, 36\, ;+\infty \, )\\\\{}\ \ \ e)\ \ \ \sqrt{x^2}\ \ \to \ \ \ x^2\geq 0\ \ \to \ \ \ x\in (-\infty ;+\infty )$

$3)\ \ a)\ \ \sqrt{x}=5\ \ \ \to \ \ \ x=25\\\\{}\ \ \ b)\ \ 6\sqrt{x} =1\ \ \ \to \ \ \sqrt{x}=\dfrac{1}{6}\ \ ,\ \ \ x=\dfrac{1}{36}\\\\{}\ \ \ c)\ \ \sqrt{x}+9=3\ \ \ \to \ \ \ \sqrt{x}=-6\ \ \to \ \ \ x\in \varnothing$