Đáp án+Giải thích các bước giải:
1,
a,
`\sqrt{5x-2}`
`Đk:5x-2≥0⇔5x≥2⇔x≥\frac{2}{5}`
b,
`\sqrt{\frac{3x-1}{5}}`
`Đk:`
`\frac{3x-1}{5}≥0`
`⇔3x-1≥0`
`⇔3x≥1`
`⇔x≥\frac{1}{3}`
c,
`\sqrt{\frac{3}{15-2x}}`
`Đk:`
$\begin{cases}\dfrac{3}{15-2x}≥0\\15-2x\neq0\end{cases}$
`⇔15-2x>0`
`⇔15>2x`
`⇔\frac{15}{2}>x`
d,
`\sqrt{\frac{-2x}{x^2-3x+9}}`
`Đk:`
$\begin{cases}\dfrac{-2x}{x^2-3x+9}≥0\\x^2-3x+9\neq0\end{cases}$
$⇔\begin{cases}\dfrac{-2x}{x^2-3x+9}≥0\\(x-\dfrac{3}{2})^2+\dfrac{27}{4}\neq0\end{cases}$
`⇔-2x≥0`
`⇔x≤0`
2,
a,
`\sqrt{\frac{196}{625}}`
`=\sqrt{\frac{2^2 .7^2}{5^4}}`
`=\frac{2.7}{5^2}`
`=\frac{14}{25}`
b,
`\sqrt{7^2}=7`
c,
`\sqrt{\frac{1}{3}}.\sqrt{\frac{1}{27}}`
`=\sqrt{\frac{1}{3}.\frac{1}{27}}`
`=\sqrt{\frac{1}{81}}`
`=\frac{1}{9}`
d,
`\sqrt{6,4}.\sqrt{250}`
`=\sqrt{6,4.250}`
`=\sqrt{64.25}`
`=8.5`
`=40`
3,
a,
`\sqrt{(3-\sqrt{10})^2}`
`=|3-\sqrt{10}|`
`=\sqrt{10}-3`
b,
`\frac{-1}{y}\sqrt{xy^2}(y<0)`
`=\frac{1}{y}.y\sqrt{x}`
`=\sqrt{x}`
