Determine the exact value of (Square Root of Square Root)

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SUMMARY

The discussion centers on solving the equation defined by the infinite nested radical expression \( x = \sqrt{10 + \sqrt{10 + \sqrt{10 + \ldots}}} \). Participants confirm that squaring both sides leads to the equation \( x^2 = 10 + x \). This can be rearranged to form the quadratic equation \( x^2 - x - 10 = 0 \). The solutions to this equation yield the exact value of \( x \), which is \( \frac{1 \pm \sqrt{41}}{2} \).

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  • Understanding of quadratic equations
  • Familiarity with nested radicals
  • Basic algebraic manipulation skills
  • Knowledge of the quadratic formula
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  • Practice solving quadratic equations using the quadratic formula
  • Explore the convergence of infinite series and sequences
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Students studying algebra, mathematics enthusiasts, and anyone interested in solving complex equations involving nested radicals.

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Determine the exact value of... (Square Root of Square Root)

I was looking through my textbook and saw a interesting question, I attempted but couldn't get it. (The Answer in Back of Text Book Was Different From Mine..)

Question
Determine the exact value of...

√10+√10+√10...


I tried typing it as well as I can , I uploaded image of question just in case :D

Determine the exact value of:
0sVBk.jpg
 
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Let

x=\sqrt{10+\sqrt{10+\sqrt{10+...}}}

What is

x^2-10

Does this give you an equation that you can solve??
 

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