Adverb, Noun, and な adjective
いがい
意外にも、父はすぐにさん成してくれました。
Unexpectedly, my dad approved of it right away.
ゆですぎのやわらかいパスタをこのんで食べるのは、カナダの意外な文化でした。
Liking soft pasta that's been cooked too long was an unexpected aspect of Canadian culture.
フグは物凄く走るの速いよ。海ではあまり良いスイマーじゃなかったってことと、大学に入るまで陸上での競技に出たことがなかったってのは、本当に意外だよ。
Fugu is a really fast runner. The surprising thing is, he was never a good swimmer in the sea and never raced on land until he was in college.
Something outside your normal idea of how things work will come as unexpected to you.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.