@marcusmathstutor: √2 or ∛3. Which is bigger? They’re incredibly close, so decimal approximations aren’t very satisfying. But there’s a neat way to compare them exactly, without a calculator. The key is turning both roots into powers you can compare directly.
i thought that that’s a square root, why’d u call it a quadratic root?
2026-08-21 22:10:43
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Petros Markadas :
if a^b > c^b , it doesn't necessarily means that a > c . This true only when a and c are greater than 1. In order for this proof to be complete, it should also be mentioned that both 2^(1/2) and 3^(1/3) are greater than 1.
2026-08-21 17:03:14
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Triangle :
Why we saying 'quadratic root' bro
2026-08-23 01:22:37
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petersimpson58 :
beautiful
2026-09-14 00:29:50
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DailySnippets :
Take 3d power on both sides… 2*1.41<3 no need to make things too complicated
2026-08-22 05:40:59
3
thomasroyal1 :
Is it always the case that a^(1/a) < b^(1/b) if a
2026-08-21 21:37:53
0
Mhlengi Ngwenya :
that still not 9 it is 9^1/3
2026-08-22 10:44:39
1
loganeide1 :
Would it be simpler to think root(1,1)=1 < root(2,2)=1.something (so following pattern) < root(3,3)? Could be wrong tho
2026-08-22 03:14:50
0
sun jin woo irl :
2^1/2
3^1/3
2^1/2=3^1/3 no but yh
put everything to the power of like 6
2^3=3^2
8=9 so the 3 one
2026-08-21 17:35:44
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johnmiller2599 :
try to take them both to the power of 6. 2^3 = 8 < 3^2 = 9
2026-08-23 17:35:11
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kma815 :
What sucks about this question is when I tried to do the calculus on the function y=x^(1/x) the only thing I learned is that e is the maximum which did not help me at all!!!
2026-08-21 17:25:09
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BIGSWAN :
that was easier than i expected
2026-08-22 03:33:52
1
נהוראי🥷 :
why not begin with power 6 ?
2026-08-22 11:24:23
3
Shere Khan :
According to my ruthless 9th grade math teacher, there are only two methods of comparing: 1. Subtract and compare to 0; and 2. Divide and compare to 1. Let’s see method #2
E = 2^0.5 / 3^0.3, E > 0 =>
E^6 = 2^3/ 3^2 =>
E^6 = 8/9 =>
E^6 E
2^0.5 < 3^0.3
2026-08-21 19:00:05
1
Nigel Coldwell :
why can't you cube and square both sides?
2026-08-21 18:39:15
2
SamTeachesMaths :
would it also be valid to compare 2^3/6 and 3^2/6. As such you'll end up with the 6th root of 8, compared to the 6th root of 9.
2026-08-21 15:45:22
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yasir :
Cube both sides to 2sqrt2 which is roughly 2x1.41 compared to 3 which 2.82 and 3 so you know that the cube root of the 3 is bigger
2026-08-21 19:40:25
2
Domino :
^6
2³ < 3²
2026-08-30 23:32:48
0
Makinen :
Intuition says root 2 before watching
2026-08-24 07:07:37
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earnies08 :
In step 2 you state ‘square both sides. That implies that you have an equation or an inequality. You don’t have that in this case so when you say square both sides, what does that mean?
2026-08-23 23:34:58
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niko :
2^(1/2)=2^(3/6)=8^(1/6)<9^(1/6)=3^(2/6)=3^(1/3)
2026-08-23 18:22:11
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carpe diem :
mcm index 6
2026-08-23 05:31:04
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Daniel Halevi :
If you take the function f(x)=x^(1/X) the Max value will be at e, e^1/e.
2026-09-03 10:23:18
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