Simplifying A Radical Expression | Three Methods

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Simplifying A Radical Expression in Three Ways
#radicalequations #radicals
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[shmuelzehavi]

The second method is the simplest and most natural one for such a trivial problem.

[mcwulf]

Darn! I spotted the cube in the numerator but didn't spot the factorisation 🤦‍♂️. Then used your method 1.

[scottleung]

The second method was quick and brilliant!

[littlekeung]

2nd method & 3rd method are almost the same, but substitution make 2nd method (& difference of 2 cube formula ) easier to handle.

[septembrinol]

I would try a substitution. (u = √x, v = √y). That would give me u^3 - v^3, which factors as (u-v)(u^2+ uv + v^2) in the numerator, and the second factor in the denominator, then I'd get u-v = √x-√y.. I haven't watched the video yet. I will comment more on it later, if feel like doing it.

[tryingtomakeanamebelike]

Method
x=a^2
y=b^2

(a^3 - b^3)/(a^2 + ab + b^2)
Factor
(a-b)(a^2 + ab + b^2)/(a^2 + ab + b^2)
a-b
root(x) - root(y)

[Hobbitangle]

Seems to be very simple after the quite obvious substitution:
x = v² and y=w²;
(v³-w³)/(v²+v•w+w²)=
(v-w)•(v²+v•w+w²)/
(v²+v•w+w²)=v-w=√x-√y

[KNOCK_OUT_]

Hey please work on consept for each question please .