Mastering Simplification of Square Roots with Multiple Terms

In summary, the conversation discussed simplifying expressions involving square roots and the relationship between the square root of a number and the number itself. This was demonstrated through examples such as (√3*√3*√3)/(√3+√3+√3) and √3+√3+√3 = 3√3. The conversation also touched on the definition of square roots and how it relates to the simplification of expressions.
  • #1
Phycisists
39
0
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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  • #2
√3*√3 = ?
 
  • #3
√9, but I don't understand hpw to simplify when it's +...
 
  • #4
: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 ?
 
  • #5
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.
 
  • #6
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?
 
  • #7
I think that quite a few people never learn or forget that:

[tex]\overbrace{x + x + \ \dots + x}^{n \ times} = nx[/tex]
 

FAQ: Mastering Simplification of Square Roots with Multiple Terms

What is the process for adding square roots?

To add square roots, you first need to find the square root of each number being added. Then, you can combine any like terms, such as the numbers under the radical sign. Finally, simplify the result if possible.

Can square roots be added if they have different radicands?

No, square roots can only be added if they have the same radicand. If the radicands are different, you will need to simplify them first before adding.

How do I simplify square roots before adding them?

To simplify square roots, you need to find the largest perfect square that is a factor of the radicand. Then, you can take the square root of that perfect square and bring it outside of the radical sign. The remaining numbers under the radical sign can be combined with like terms.

Is it possible to add more than two square roots?

Yes, you can add more than two square roots by following the same process of finding the square root of each number, combining like terms, and simplifying the result.

Can I use a calculator to add square roots?

Yes, you can use a calculator to add square roots. Most scientific calculators have a square root function that can help with simplifying and adding square roots.

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