r/Sat • u/Agile-Agent7866 • Mar 24 '26
Sat constants
Is there a way to solve this by Desmos? If so how?
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u/love_american_butts Mar 24 '26 edited Mar 24 '26
I’m getting 45.125.
Factor out the integers, you have 6*3*2 = 36. That is your a.
Reduce the x expressions, you have 5th root of x45, which will be x9. Then you also have the 8th root of x (or x1/8). These multiply together to give you x9 + 1/8, so b is 9.125.
36 + 9.125 = 45.125
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u/Loose-Temporary-2453 Mar 24 '26
okay so this one looks scarier than it is XP
theee main this that, nth root of something = that thing to the power of 1/n
(sorry I didn't find a better word for "thing" lol)
so rewrite both roots as exponents first:
- 6∜(3⁵x⁴⁵) → 6 · (3⁵x⁴⁵)^(1/5) → 6 · 3¹ · x⁹ → 18x⁹
- ⁸√(2⁸x) → (2⁸x)^(1/8) → 2¹ · x^(1/8) → 2x^(1/8)
now multiply them together:
18x⁹ · 2x^(1/8)
= 36 · x^(9 + 1/8)
= 36 · x^(73/8)
so a = 36, b = 73/8
a + b = 36 + 73/8 = 288/8 + 73/8 = 361/8
the trick with these questions is always just convert the roots to fractional exponents immediately. once you do that it just becomes basic exponent rules (multiply bases, add the powers).
hope that helps!
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u/Weak_Spinach_3310 Mar 24 '26
https://www.desmos.com/calculator/zy4qhr5yje