てごらん

てごらんte gorancasual

savor + (and…) + go on and do it — a coaxing instruction aimed downward

ajiwatte goran

go on and do it — a coaxing instruction aimed downward

meaning: go on and savor

これ、一口ひとくち味あじわってごらん。すごくおいしいから。

kore, hitokuchi ajiwatte goran. sugoku oishii kara.

Here, go on and savor a bite of this — it's really good. casual

ちょっとこっち来きて、窓まどの外そと見みてごらん。

chotto kotchi kite, mado no soto mite goran.

Come over here a second and look outside the window. casual

All examples4

go on and do it — inviting someone below you to try it

これ、一口ひとくち食たべてごらん。すごくおいしいから。
kore, hitokuchi tabete goran. sugoku oishii kara.
Here, go on and eat a bite of this — it's really good. casual
ちょっとこっち来きて、窓まどの外そと見みてごらん。
chotto kotchi kite, mado no soto mite goran.
Come over here a second and look outside the window. casual
難むずかしく考かんがえないで、まず自分じぶんの言葉ことばで書かいてごらん。
muzukashiku kangaenaide, mazu jibun no kotoba de kaite goran.
Don't overthink it — just write it in your own words first. neutral
本当ほんとうかどうか、一度いちど自分じぶんの目めで確たしかめてごらんなさい。
hontou ka dou ka, ichido jibun no me de tashikamete goran nasai.
Go and check with your own eyes whether it's true. neutral

てごらんなさいtegorannasaialternant
味あじわってごらんなさい
the unclipped form — a teacher or a parent giving the instruction properly, a shade sterner and further from the listener than bare ごらん.
てごらんよtegoran'yocolloquial
味あじわってごらんよ
よ pushes the coaxing further, for talking someone into it — 一口ひとくちだけ食たべてごらんよ。

Written in kana: ごらん is the honorific ご覧らん with the respect bleached
out, so 見みてごらん is normal despite the doubling. Aimed upward it
condescends.