The Root of the Problem: Solving a Nested Square Root Equation by Applying Exponent Rules
I saw an interesting nested square root equation, and while I like the original creator's take (you can see their video below), I think it works a little bit better to convert the radical form expressions to exponential form and simplify from there.
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I prefer simplifying here with exponent rules, which means that we need to use the exponential equivalent to the square root radical: the one-half power. Re-writing the nested radicals as repeated one-half powers allows us to combine the terms by either adding exponents together, applying the product of powers rule, or by multiplying exponents, applying the power of a power rule.
Finally, at the end, we have x to the 7/8 power equals 7, so we can raise each side of the equation to the 8/7 power in order to isolate x and get our solution at x equals 7 to the 8/7 power. Alternatively, if we prefer, we can convert that back into radical form and have x equals the 7th root of 7 to the eighth power.
Original Video: https://www.tiktok.com/t/ZTLdPyT4F/
#ExponentRules #RadicalToExponential #AlgebraSimplified
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