What is the value of this crazy iterated square??

🌟To get started for free, visit https://brilliant.org/MichaelPenn/
🌟Support the channel🌟
Patreon: https://www.patreon.com/michaelpennmath
Merch: https://teespring.com/stores/michael-penn-math
My amazon shop: https://www.amazon.com/shop/michaelpenn

🟢 Discord: https://discord.gg/Ta6PTGtKBm

🌟my other channels🌟
Course videos: https://www.youtube.com/channel/UCC6Wl-xnWVS9FP0k-Hj5aiw
non-math podcast: https://www.youtube.com/channel/UCIl9oLq0igolmqLYipO0OBQ

🌟My Links🌟
Personal Website: http://www.michael-penn.net
Instagram: https://www.instagram.com/melp2718/
Randolph College Math: http://www.randolphcollege.edu/mathematics/
Research Gate profile: https://www.researchgate.net/profile/Michael_Penn5
Google Scholar profile: https://scholar.google.com/citations?user=W5wkSxcAAAAJ&hl=en

🌟How I make Thumbnails🌟
Canva: https://partner.canva.com/c/3036853/647168/10068
Color Pallet: https://coolors.co/?ref=61d217df7d7058000b2f880c

🌟Suggest a problem🌟
https://forms.gle/ea7Pw7HcKePGB4my5

math mathematics number theory abstract algebra calculus differential equations Randolph College randolph Michael Penn continued fraction brain teaser nested radical square root of 2 newtons method