Fast shortcut for nested square roots (plus the proof)

We will learn how to simplify nested square roots using a nice shortcut. We will do 3 quick examples and then see the proof of the shortcut. Subscribe to @bprpmathbasics for more algebra tutorials.

0:00 The fast way to simplify nested square roots
1:40 The proof of the shortcut

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#math #algebra #mathbasics

[newme]

This saved me today. I went to the super market and bought lunch but the total came to √ (5 +2√6). as I only had √3 + √2
I slapped it down on the counter and said, "Go check YouTube that's the correct amount" :)

[annie-kjls]

thank you for all the hard work you put into your videos they have made me become so interested in maths !

[garrettbates]

Neat. I would have never thought of approaching these problems in this way, and I don't remember learning it in algebra, though I could have just forgotten. I tend to just approximate whenever i see a root these days, so that I don't need to reach for a calculator so often.

[cyrusyeung]

Note that a and b cannot be *both* negative. If a = b = - 1, √(a + b + 2√(ab)) = 0, but √a + √b = 2i. They are not equal.

[holyshit]

Quite easy to guess
5+2=7, 5*2 = 10
7+3 = 10, 7*3 = 21
7+4 = 11, 7*4 = 28

[NuzranRahat]

what if I had some number besides 2 (like 7? ). And how can I make that into 2?

[m.h.]

While I agree, that it is a nice 'shortcut', it is essentially useless information and equivalent to me telling someone from Australia, that there is a shortcut in my backyard in Germany.
Hardly ANYONE will ever be in a place to use it ONCE, let alone regularly.

[anassayed]

Why does the shirt say algebra, but arabic?
Do u speak arabic or what, just curious?