My math teacher asked us this for extra credit:
What is the square root of 1 of the square root of 1 of the square root of 1... and it keeps repeating. He said it would be an irrational number.
2007-01-28 04:37:59 · 10 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
I figured it would be 1 but that's not an irrational number.
2007-01-28 04:44:15 · update #1
Of course, you mistated the question. It's supposed to be, "What's the square root of 1 PLUS the square root of 1 PLUS, etc.?" The expression is supposed to be:
x = √ (1+(√ 1+(√ 1+... ...)))
Square both sides to get:
x ² = 1+√ (1+(√ 1+(√ 1+... ...))) = 1 + x, or
x ² - x - 1 = 0
We use the formula for finding roots of the quadratic equations, which is of the general form (where a x ² + b x + c = 0):
x = (1/2a) (-b ± √(b² -4ac))
Since a = 1, b = -1, c = -1, we have:
x = (1/2)(1 ± √(1 +4)), or, choosing the positive root, we have
x = 1/2(1+√ 5) = 1.618..., which is the famous Golden Ratio.
Below are a couple of helpful wiki articles.
2007-01-28 04:55:30 · answer #1 · answered by Scythian1950 7 · 2⤊ 0⤋
1
2007-01-28 04:44:30 · answer #2 · answered by Laureneliz 3 · 0⤊ 0⤋
The square root of 1 of the square root of 1 of... does not make sense mathematically ! For example what would the square root of 2 of the square root of 3 mean?
Did the teacher mean to say the square root of the square root of the square root of the ....square root of 1 ? In this case the answer would be 1 like everyone says. Is negative one also an answer in this case as -1 x -1 = +1 also?
2007-01-28 05:00:34 · answer #3 · answered by ignoramus_the_great 7 · 0⤊ 0⤋
It is 1 because the square root of one is one and you cant break that down any further
2007-01-28 04:45:01 · answer #4 · answered by Patricia K 2 · 0⤊ 0⤋
1
The square root of 1 is 1, or no matter how many times you take the square root it will be 1.
2007-01-28 04:42:40 · answer #5 · answered by Richard 7 · 0⤊ 0⤋
Well, it's possible that he didn't make it clear what he was really talking about. There are similar continued fraction expressions which do converge to irrational numbers.
Or
Maybe he's wrong! It can happen. Teachers arn't perfect.
Or
You didn't quite understand what he meant. Actually this and the first one can be combined into a 'misunderstanding between both of you'.
2007-01-28 04:54:42 · answer #6 · answered by modulo_function 7 · 0⤊ 0⤋
The sq root (1) = 1, the sq root [sq root(1)] = sq root [1] = 1. We can do this indefinitely, the answer will always be 1.
2007-01-28 04:50:21 · answer #7 · answered by flyfisher_20750 3 · 0⤊ 0⤋
Unless I'm mistaken:
limit as n--> infinity [(1)^(1/2)^n]
limit as n--> infinity [1]^n = 1
So the answer should be 1.
2007-01-28 04:52:14 · answer #8 · answered by ybdogsct 2 · 0⤊ 0⤋
x=9.9 10x=ninety 9 youre precise up until eventually this next step. (10x)-x=ninety you cant only subtract x from one area and subtract 10 from the different? you go with to subtract the same component from each and every area. (9x)/9=ninety/9 x=10 9.9=10
2016-10-16 05:28:05 · answer #9 · answered by vergeer 4 · 0⤊ 0⤋
the answer is till 1
use your brain, just because he said it's an irrational number, doesn't mean it must be an irrational number.
2007-01-28 04:41:41 · answer #10 · answered by 7 · 0⤊ 0⤋