What is the difference between Root and Route and Rout?

What is the difference between Root and Route and Rout? :

Root : (noun)

1 ) Part of the plant that keeps it firmly in the soil and absorbs water and food from the soil

This is a plant with long roots.

2 ) Family ties, feelings, etc…that attach a person emotionally and culturally to the society or community where he grew up and / or lives or where his ancestors lived

She has no real root in this area.

They are totally cut off from their peasant roots.

Many Americans have root in Europe.

3 ) Source or basis

The root of the problem is lack of trust.

Money is often said to be the root of all evil.

Root : (verb)

1 ) Send down roots and begin to grow

This type of plant roots easily.

2 ) Plant something

Root the cuttings in peat.

3 ) Cause someone to stand fixed and unmoving

He stood rooted to the spot.

Fear rooted him to the spot.

4 ) Establish something deeply and firmly

Her love for me is deeply rooted.

This is a story firmly rooted in reality.

Route : (noun)

1 ) Way taken or planned to get from one place to another

We drove home by a roundabout route.

Route : (verb)

1 ) Send something by a specified route

This flight is routed to Kolkata via Patna.

Rout : (noun)

1 ) Utter defeat ending in disaster

After our fourth goal, the match became a rout.

The terrified army fled in rout.

Rout : (verb)

1 ) Defeat someone completely

Make someone retreat in confusion

The Prime Minister resigned after his party was routed in the election.

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