This is for advanced calculus at the college level. Are 2^sqrt(2) and sin(sqrt(2

Question

This is for advanced calculus at the college level.
Are 2^sqrt(2) and sin(sqrt(2)) numbers?"Do they exist?" How are they defined? How can one calculate them?


I want to say that of course they are numbers, but I am not really sure because I feel like it would not be a question if it was that easy. Can anyone please help me? Thanks in advance. This is for advanced calculus at the college level.
Are 2^sqrt(2) and sin(sqrt(2)) numbers?"Do they exist?" How are they defined? How can one calculate them?


I want to say that of course they are numbers, but I am not really sure because I feel like it would not be a question if it was that easy. Can anyone please help me? Thanks in advance. This is for advanced calculus at the college level.
Are 2^sqrt(2) and sin(sqrt(2)) numbers?"Do they exist?" How are they defined? How can one calculate them?


I want to say that of course they are numbers, but I am not really sure because I feel like it would not be a question if it was that easy. Can anyone please help me? Thanks in advance. This is for advanced calculus at the college level.
Are 2^sqrt(2) and sin(sqrt(2)) numbers?"Do they exist?" How are they defined? How can one calculate them?


I want to say that of course they are numbers, but I am not really sure because I feel like it would not be a question if it was that easy. Can anyone please help me? Thanks in advance. This is for advanced calculus at the college level.
Are 2^sqrt(2) and sin(sqrt(2)) numbers?"Do they exist?" How are they defined? How can one calculate them?


I want to say that of course they are numbers, but I am not really sure because I feel like it would not be a question if it was that easy. Can anyone please help me? Thanks in advance. This is for advanced calculus at the college level.
Are 2^sqrt(2) and sin(sqrt(2)) numbers?"Do they exist?" How are they defined? How can one calculate them?


I want to say that of course they are numbers, but I am not really sure because I feel like it would not be a question if it was that easy. Can anyone please help me? Thanks in advance. This is for advanced calculus at the college level.
Are 2^sqrt(2) and sin(sqrt(2)) numbers?"Do they exist?" How are they defined? How can one calculate them?


I want to say that of course they are numbers, but I am not really sure because I feel like it would not be a question if it was that easy. Can anyone please help me? Thanks in advance. This is for advanced calculus at the college level.
Are 2^sqrt(2) and sin(sqrt(2)) numbers?"Do they exist?" How are they defined? How can one calculate them?


I want to say that of course they are numbers, but I am not really sure because I feel like it would not be a question if it was that easy. Can anyone please help me? Thanks in advance. This is for advanced calculus at the college level.
Are 2^sqrt(2) and sin(sqrt(2)) numbers?"Do they exist?" How are they defined? How can one calculate them?


I want to say that of course they are numbers, but I am not really sure because I feel like it would not be a question if it was that easy. Can anyone please help me? Thanks in advance. This is for advanced calculus at the college level.
Are 2^sqrt(2) and sin(sqrt(2)) numbers?"Do they exist?" How are they defined? How can one calculate them?


I want to say that of course they are numbers, but I am not really sure because I feel like it would not be a question if it was that easy. Can anyone please help me? Thanks in advance. This is for advanced calculus at the college level.
Are 2^sqrt(2) and sin(sqrt(2)) numbers?"Do they exist?" How are they defined? How can one calculate them? This is for advanced calculus at the college level.
Are 2^sqrt(2) and sin(sqrt(2)) numbers?"Do they exist?" How are they defined? How can one calculate them?


I want to say that of course they are numbers, but I am not really sure because I feel like it would not be a question if it was that easy. Can anyone please help me? Thanks in advance.

Explanation / Answer

Remember numbers doesn't mean just 1,2,3,4.. and i'm sure you know it.

1,2,3,4.. are natural numbers.

To avoid confusion i will give you details

1,2,3,4,5 ... are natural numbers (N)

-infinity......-5,-4,-3,-2,-1,0,1,2,3,4,5....+infinity are whole numbers (W)

any number of the form p/q where p,q are integers are called rational numbers (Q)

Now, any numbers other than these are included in Real numbers (R)

Now Coming to 2^sqrt(2)

Sqrt(2) is a number which upon squaring(raising to power 2) gives 2

(It has infinite digits. The more number of digits you use more accurate you will be!)

Similarly,

2^sqrt(2) is is a number which is 2 multplied sqrt2 times

You might wonder how 2 can be multiplied sqrt(2) times, 2 can be multiplied 1,2,3... times only!

Thats incorrect. Logically that can be done!

sqrt(2) keeps going like this 1.414213562....

If i use these many i will get 2^(1.414213562)

the more digits you use more accurate you will be

2^sqrt(2) = 2.665144143..

And remember many things that scientists or mathematicians do are pretty accurate but not exact.They are too micoscopic (smaller or negligible).

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.