Mastering Simplification of Square Roots with Multiple Terms

[Phycisists]

How do I solve, 1:

(√3*√3*√3)/(√3+√3+√3)? How do I simplify it? I'm confused on how to shorten √x+√x+√x, I just don't get it.

Also if:

√700 = 26.46, then how is √70000 = 264.6? Shouldn't it be 2646?

 

[voko]

√3*√3 = ?

 

[Phycisists]

√9, but I don't understand hpw to simplify when it's +...

 

[BvU]

orange + orange + orange = 3 oranges.
Similarly √3+√3+√3 = 3√3

Voko would have liked it a lot better if you would have typed a number, not an expression... How much is √9 ?

 

[Nugatory]

√700 = 26.46, then how is √70000 = 264.6? Shouldn't it be 2646?

Try writing 70000 as 700*100, see where that gets you.

 

[Ray Vickson]

√9, but I don't understand hpw to simplify when it's +...

Really? Go back and think about the DEFINITION of √3, or √n for any number n. In other words, when we speak of the number r = √n, what is the fundamental relationship between r and n?

 

[PeroK]

I think that quite a few people never learn or forget that:

$$\overbrace{x + x + \ \dots + x}^{n \ times} = nx$$