Mastering Simplification of Square Roots with Multiple Terms

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Homework Help Overview

The discussion revolves around simplifying expressions involving square roots, particularly focusing on the simplification of terms like (√3*√3*√3)/(√3+√3+√3) and understanding the relationship between square roots of different numbers, such as √700 and √70000.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore how to simplify expressions involving multiple square roots and question the arithmetic of square roots when added together. There are attempts to clarify the relationship between square roots and their respective values, as well as the implications of multiplying and adding square roots.

Discussion Status

The discussion includes various attempts to clarify the simplification of square roots and the arithmetic involved. Some participants provide insights into the definitions and properties of square roots, while others express confusion about specific simplifications and relationships.

Contextual Notes

Participants are grappling with the definitions and properties of square roots, particularly in the context of addition and multiplication. There is also a mention of potential misunderstandings regarding the scaling of square roots with respect to their numerical values.

Phycisists
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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?
 
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√3*√3 = ?
 
√9, but I don't understand hpw to simplify when it's +...
 
:smile: 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 ?
 
Phycisists said:
√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.
 
Phycisists said:
√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?
 
I think that quite a few people never learn or forget that:

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

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