Correct

睡 vs 睡觉

/ shuì vs shuìjiào /
Strokes

Definition

睡 is a Verb, 睡觉 is a Verb-object phrase, which means [sleep].

Example

睡 is used to show ordinary sleep as in examples, not 睡觉. 睡 is especially used here in contrast with 起, or with the complement of 到, so only 睡 can be used.
1
Zǎoshuì
早睡
zǎo
早起
  
,
shēn
身体
hǎo
  

Early to bed and early to rise is good for your health.

2
jīntiān
今天
zhí
一直
shuì
dào
shàng
上午
10
10
diǎn
cái
lai
起来
  

He didn't get up this morning until 10 o'clock.

觉 in 睡觉 is the object but with the sense of a measure word.
3
tài
lèi
le
  
,
tǎng
zài
bǎn
地板
shàng
jiù
shuì
le
jiào
  

He was too tired and slept on the floor.

4
Zhù
shuì
hǎo
jiào
  

I hope you have a sound sleep.

5
Shuì
le
jiào
lai
起来
  
,
tóunǎo
头脑
hěn
qīngshuǎng
清爽
  

You will feel fresh after a sound sleep.

睡 and 睡觉, both words can take 着 (zháo), meaning "asleep".
睡着(zháo)觉 is used in examples ⑨ and ⑩ because falling asleep is especially emphasized.
6
gāng
tǎng
xià
jiù
shuìzhāo
睡着
le
  

She fell asleep as soon as she went to bed.

7
fān
lái
  
,
zěnme
怎么
shuì
zhāo
  

He tossed all night long.

8
bàntiān
半天
méi
shuìzhāo
睡着
  

After a long time, he couldn't go to sleep yet.

9
zǒngshì
总是
shīmián
失眠
  
,
guǒ
如果
néng
tǎng
xià
jiù
shuìzhāo
睡着
jiào
jiù
hǎo
le
  

I'm always sleepless. If only I could go to sleep!

10
Zuìjìn
最近
zěnme
怎么
lǎo
shuì
zhāo
jiào
ne
  
?

Why not be able to go to sleep recently?

睡 and 睡觉 are interchangeable sometimes, if nothing is stressed.
11
jīng
已经
shuì
  
(
shuìjiào
睡觉
  
)
le
  
,
míngtiān
明天
zài
lái
  

He's asleep, please come here tomorrow.

12
Tiān
天气
shi
hěn
lěng
de
shíhou
时候
  
,
zǒngshì
总是
kāi
zhāo
chuānghu
窗户
shuì
  
(
shuìjiào
睡觉
  
)
  

He sleeps with the window open unless it's really cold.