Easy question about the root (of a real number)

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In summary, the conversation discusses a question about finding the root of a real number. The solution involves using clever thinking and solving the equation \sqrt{3-2\sqrt{2}}=\sqrt{2}-1 as is, which leads to the relationship between \left(2-2\sqrt{2}+1\right) and \left(\sqrt{2} - 1\right). The conversation ends with the person apologizing for taking up the others' time, but they assure them that it was not a waste.
  • #1
joris_pixie
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[SOLVED] Easy question about the root (of a real number)

Hi, I'm a bit embarresed to ask this but does anybody know how to get this:
[tex]\sqrt{3 - 2\sqrt{2}} = \sqrt{2} - 1[/tex]

?
 
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  • #2
joris_pixie said:
Hi, I'm a bit embarresed to ask this but does anybody know how to get this:
[tex]\sqrt{3 - 2\sqrt{2}} = \sqrt{2} - 1[/tex]

?
[tex]\sqrt{3 - 2\sqrt{2}}=\sqrt{2-2\sqrt{2}+1}[/tex]

what is the relationship between [tex]\left(2-2\sqrt{2}+1\right)[/tex] and [tex]\left(\sqrt{2} - 1\right)[/tex]??
 
  • #3
I must say that this one does require a bit of clever thinking. I can add that the best way to "see" the answer is to take your equation

[tex]\sqrt{3-2\sqrt{2}}=\sqrt{2}-1[/tex]

and solve it as is (this will ultimately lead you to what S_David is pointing out).
 
  • #4
OK! Got it !
Sorry for wasting your time and thank you ! :)

phyzmatix said:
This one does require a bit of clever thinking I must say. I can add that the best way to "see" the answer is to take your equation

[tex]\sqrt{3-2\sqrt{2}}=\sqrt{2}-1[/tex]

and solve it as is (this will ultimately lead you to what S_David is pointing out).

It's true that it is one you have to 'see' !
And if you 'see it' it's easy, but if you don't ...

But thanks a lot you guys, got it now!
 
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  • #5
joris_pixie said:
OK! Got it !
Sorry for wasting your time and thank you ! :)

Definitely didn't waste my time. You forced me to think, which is always good! :biggrin:
 

Related to Easy question about the root (of a real number)

What is the definition of a "root" of a real number?

A root of a real number is a number that, when multiplied by itself a certain number of times, gives the original number. For example, the square root of 25 is 5 because 5 multiplied by itself (5 x 5) equals 25.

What is the difference between a "square root" and a "cube root"?

A square root is a number that, when multiplied by itself, gives the original number. A cube root is a number that, when multiplied by itself twice, gives the original number. For example, the square root of 16 is 4 because 4 x 4 = 16. The cube root of 8 is 2 because 2 x 2 x 2 = 8.

How do you find the square root of a real number?

To find the square root of a real number, you can use a calculator or estimate it by finding the closest perfect square that is less than the original number. Then, you can use long division or a similar method to find the square root.

What is the symbol for a square root?

The symbol for a square root is √ (called a radical symbol), which comes from the Latin word "radix" meaning "root".

Can negative numbers have a square root?

Yes, negative numbers can have a square root. However, the result will be a complex number, which is a combination of a real number and an imaginary number. For example, the square root of -4 is 2i, where i is the imaginary unit (√-1).

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