Discrete Math: Prove that 2^n is greater than n squared where n is an integer greater than 4.

In this video we prove by induction that 2^n is greater than n^2 where n is an integer greater than 4. This question is taken from Discrete Mathematics and Its Applications by Kenneth Rosen. 7th Edition. Chapter 5.1. Question 21.

Discrete Mathematics and Its Applications playlist:
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Induction Proofs playlist:
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Chapters:
00:00 Introduction to the Question
01:04 Base Case P(5)
01:50 Inductive Step
02:10 Induction Hypothesis (IH) P(k)
02:57 Building Inequalities, The General Idea
04:00 We Want to Show P(k+1) Case
04:53 Starting with the LHS
08:05 Induction Proof Within an Induction Proof?!?! NO!!
12:03 Building the Inequalities
12:25 Putting It All Together
14:04 QED and Thanks for Watching

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