I updated my iPhone and now it won't download apps?

My phone said it was ready for a software update and ever since I can't download apps. I thought the update must have taken up a lot of memory so I deleted 9 apps, over 600 photos, and over an hour of music but still no luck!
I go to click download in the App Store, I'm prompted to type in my password and then it just never downloads.
Any help greatly appreciated!

Turn it off then back on after 30 sec. Souls start be able to download.

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