Let's give him a big hand.

Let's give a big hand to him.
Let's applaud him.
Let's give him a round of applause.
Let's give a rould of applause to him.

(Are they all the same in meaning?)

All ae okay.

The sentences with 'to him' in them would be less used, but all are correct.

Yes, in terms of overall meaning, all of the phrases convey the same message. They are all expressions used to encourage an audience or group of people to applaud or show appreciation for someone. However, there are slight differences in the way the sentences are constructed:

1. "Let's give him a big hand" - This phrase is a common way to ask people to clap their hands and show their appreciation for someone. It emphasizes the action of applauding.

2. "Let's give a big hand to him" - This phrase has the same meaning as the previous one but places more emphasis on the recipient, as it explicitly mentions "to him."

3. "Let's applaud him" - This is a more general phrase that suggests clapping as a way to acknowledge or recognize someone.

4. "Let's give him a round of applause" - This phrase is similar to the first two, but instead of just a "big hand," it suggests a sustained applause, typically lasting longer than a simple clapping gesture.

5. "Let's give a round of applause to him" - This phrase has a similar meaning to the fourth one, but again emphasizes the recipient by mentioning "to him."

Overall, while there may be slight differences in emphasis or the specific wording, these phrases are commonly used interchangeably to request or encourage applause for someone.