Dear Bprp, I have a pretty unusual question: If sqrt(a+sqrt(a+sqrt(a)))=128, then floor(a)=? @blackpenredpen

Dear Bprp, I have a pretty unusual question: If sqrt(a+sqrt(a+sqrt(a)))=128, then floor(a)=? @blackpenredpen

Uploaded March 2025 | Updated September 2026, 2 weeks ago

Got this from a viewer, Yavuz. The question is if sqrt(a+sqrt(a+sqrt(a)))=128, then floor(a)=? Make sure you don't square both sides three times because that will result in a horrible 8th degree polynomial equation!
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Dear Bprp, I have a pretty unusual question: If sqrt(a+sqrt(a+sqrt(a)))=128, then floor(a)=?

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$First time solving an A-Level maths exam! (90 minutes, uncut) I will be doing a British A-Level further maths paper on the spot for the first time! This paper contains mainly algebra and calculus. Topics include complex numbers, hyperbolic equations, exponential equations, trigonometric identities and equations, first-order linear differential equations, determinant and the inverse of a 3x3 matrix, and more! Was I able to solve all the questions within 90 minutes? Was I able to get all the questions correct? Watch to find out. The afterward https://youtu.be/9GFUyT-D6D0 Try the paper first: https://qualifications.pearson.com/content/dam/pdf/A-Level/Mathematics/2017/Exam-materials/9fm0-01-que-20220526.pdf Big thanks to my Patrons for the full-marathon support! Ben D, Grant S, Erik S. Mark M, Phillippe S., Nicole D. 💪 Support this channel and get my math notes by becoming a patron: https://www.patreon.com/blackpenredpen 🛍 Shop my math t-shirt & hoodies: https://amzn.to/3qBeuw6 Timestamps: 0:00 A-Level further math paper from June 2022 0:58 Q1 Solving a cubic equation with complex roots 6:23 Q2 Solving a 4-th degree hyperbolic equation 15:55 Q3 Solving a first-order linear differential equation with integrating factor 21:28 Q4 Solving a series problem with natural log 28:55 Q5 Finding the determinant and the inverse of a 3x3 matrix Correction to Q5: https://youtu.be/pXdEBA6xI1c?si=11CZl3RkNheQQvMR 40:50 Q6 Partial fraction decomposition & integral of a rational function 50:05 Q7 A complex number problem 1:00:11 Q8 A long trig identity 1:23:39 Q9 An improper integral with hyperbolic cosine$

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"Dear Bprp, I have a pretty unusual question": If sqrt(a+sqrt(a+sqrt(a)))=128, then floor(a)=?