> ややきつめの目つきをしているものの根は奥手で純情な性格。

Is this right

My translation is: even though here appearance looks serious she is still
undeveloped at the core thus having an innocent personality

**

> ややきつめの目つき

** What does it mean ?
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translation
What is the translation of this sentence?
> 「ややきつめの目{め}つき」

やや ＝ 少{すこ}し ＝ slightly

きつめ ＝ きつい (harsh, intense) + め (~ish, on the ~ side)

The form is 「 **Adjective Stem + め** 」.

The confusing thing here is that this suffix め can also be written 目 in kanji.
Thus, we actually have two 目's in this phrase with only the second one meaning
"eyes".

目つき = one's look or expression

Putting it altogether, we have:

> "A look/expression that is slightly on the intense side"

Finally, your interpretation of the sentence is actually quite good.
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2019-11-01T20:48:57.010
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answer
My translation attempt is: At first glance, her appearance looks a bit stern,
but actually she is just shy and innocent.

I believe your interpretation of the sentence has no problem at all.

ややきつめの目つき means she has somewhat sharp and stern eyes, basically describing
her appearance as not very friendly-looking.

根は in this sentence means "essentially" or "actually," depicting her true
personality in the ensuing segment 奥手で純情な性格.

奥手 more literally denotes "unsophisticated," but I believe it is more close to
"shy" in the sentence.
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