@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.

Marcus
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Friday 21 August 2026 15:03:31 GMT
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morgoththefair
MorgothTheFair :
"Quadratic root" is a new term to me.
2026-08-21 15:27:18
251
bringininthebread
magic man :
just raise both sides to the power of 6
2026-08-21 20:16:57
113
_bella12312
𝐢𝐬𝐚 :
i thought that that’s a square root, why’d u call it a quadratic root?
2026-08-21 22:10:43
18
petros.markadas
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
21
triangle200
Triangle :
Why we saying 'quadratic root' bro
2026-08-23 01:22:37
3
petersimpson58
petersimpson58 :
beautiful
2026-09-14 00:29:50
0
dailysnippets8
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
thomasroyal1 :
Is it always the case that a^(1/a) < b^(1/b) if a
2026-08-21 21:37:53
0
mhlengi.ngwenya4
Mhlengi Ngwenya :
that still not 9 it is 9^1/3
2026-08-22 10:44:39
1
loganeide1
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
absbsbsbsbsbs2
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
12
johnmiller2599
johnmiller2599 :
try to take them both to the power of 6. 2^3 = 8 < 3^2 = 9
2026-08-23 17:35:11
4
therealkenadler
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
0
srsmith555
BIGSWAN :
that was easier than i expected
2026-08-22 03:33:52
1
dominiktarczynskifan
נהוראי🥷 :
why not begin with power 6 ?
2026-08-22 11:24:23
3
destrabalat
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
nigelcoldwell
Nigel Coldwell :
why can't you cube and square both sides?
2026-08-21 18:39:15
2
super.sam.schwark
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
10
yasir_2828
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
ernst.gemel
Domino :
^6 2³ < 3²
2026-08-30 23:32:48
0
regency12345
Makinen :
Intuition says root 2 before watching
2026-08-24 07:07:37
0
earnies08
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
0
nebojsaiko
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
0
ambenca
carpe diem :
mcm index 6
2026-08-23 05:31:04
0
daniel.halevi
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
0
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