Mastering Simplification of Square Roots with Multiple Terms

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SUMMARY

The discussion focuses on simplifying square roots with multiple terms, specifically the expression (√3*√3*√3)/(√3+√3+√3). Participants clarify that √3 + √3 + √3 simplifies to 3√3. Additionally, the relationship between square roots and their values is explored, highlighting that √70000 equals 264.6 because it can be expressed as √(700*100), leading to √700 * √100. Understanding the fundamental properties of square roots is essential for simplification.

PREREQUISITES
  • Understanding of square root properties
  • Basic algebraic manipulation skills
  • Familiarity with simplifying expressions involving radicals
  • Knowledge of numerical approximations of square roots
NEXT STEPS
  • Learn advanced techniques for simplifying radical expressions
  • Study the properties of square roots and their applications in algebra
  • Explore the concept of rationalizing denominators in fractions
  • Practice solving complex square root problems using numerical methods
USEFUL FOR

Students, educators, and anyone looking to enhance their understanding of algebraic simplification, particularly involving square roots and radical expressions.

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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