believe in the math, not wolframalpha

Believe in the math, not WolframAlpha. We will simplify this nested radical expression. This expression is usually from the cubic formula. Surprisingly, this expression gives us a whole number! Enjoy!

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[vinayemani]

The greatest trick humanity ever learned from mathematics - If you don't know some value, call it x and proceed.

[davidbondy]

Forget the math, I want to learn that marker-switching trick.

[georgeharamuniz]

At 13:36 you can see that wolfram alpha is assuming the principal root is being used. If you click the option to use the real-valued root instead you will get the answer of 2.

[EdDavisTeaching]

If you look just under the input box after he hits equals there is a blue box that contains the text "Assuming the principal root | Use the real-valued root instead." Click on the option for the real-valued root and it gives you 2. I do not know why Wolfram Alpha defaults to the principle root. But it will calculate the real value correctly. The same is true by the way when you use Mathematica by the way. However, I am not sure how to get Mathematica to return the real-valued root.

[TheGregstar]

When you get an integer as a root, that makes you reeeeaaaally happy.

[Jiggerjaw]

Your marker switching skills are deft af.

[VandreiganMW]

On Wolfram Alpha, you're showing the principle root. If you click "Use the Real Root instead, " you'll see your expected answer of 2.

That being said, I agree that it's bad to lean on Wolfram Alpha and Mathematica too much. But they certainly are nice tools when used correctly!

[windowsforvista]

I feel like I disappointed him every time I don't pause to try 😅

[AnalKumar]

Whoever came up with this problem is a genius

[rustamkalimullin]

Russians do like this:


Finally, (1+sqrt(2)) + (1-sqrt(2))=2.

[zweiosterei]

The marker switch game is strong in this one.

[cheeros]

Impressive black pen red pen powers at 2:00

[Robi]

I always enjoy when some complicated sq roots, cube roots etc. end up equaling some integer value :)

[felonhighman]

I believe wolfram alpha just shows you one of the correct answer, one of the complex solutions, because the cubic root of something actually leads to three results, not just one. You just can't take it as a real number for granted.

[garmrdmr]

at the top it says:
Assuming the principal root | Use the real‐valued root instead

click the blue bit.. it shows 2!
so dont complain about wolfram alpha result untilk you READ THE RESULT

[Nieznany]

2
7+5sqrt2 is 1+3sqrt2+6+2sqrt2 which is (1+sqrt2)^3 which means a=1+sqrt2
We do same for b and b=1-sqrt2
a+b=2

[maxlarose]

What really impresses me is how seamlessly you can switch between both pens. Amazing.

[georgemissailidis]

2:02 the way you swap between the black pen and red pen is so smooth, Jesus.

[walter_kunz]

In WolframAlpha you have to use the Cbrt function which is the real-valued root: And the result is "2"

[bobbmsee]

click on "Use the real‐valued root instead"