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## #1 2005-07-21 00:52:09

I love pi
Member
Registered: 2005-06-30
Posts: 11

### Square root of 0

Hi there maths chums! the other day i was relaxing upon my massaging recliner, as i needed to relieve myself of the painful rhumatism i suffer. Whilst doing so i like to ponder mathmatical problems, my mind lept upon one which caused much curiosity and admitedly a little confusion. I wonder wether any of your fine minds can enlighten me as to the square root of 0.

Last edited by I love pi (2005-07-21 00:52:54)

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## #2 2005-07-21 01:13:23

bigpaully
Member
Registered: 2005-07-20
Posts: 4

### Re: Square root of 0

sqrt (0) = 0^(1/2)

0 to any power is 0

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## #3 2005-07-21 01:13:33

MathsIsFun
Registered: 2005-01-21
Posts: 7,684

### Re: Square root of 0

Could be 0.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #4 2005-07-21 02:42:53

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Square root of 0

If a²=b, then the inverse must be true: √b=a.

0²=0, so √0=0.

Why did the vector cross the road?
It wanted to be normal.

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## #5 2005-07-21 09:45:24

MathsIsFun
Registered: 2005-01-21
Posts: 7,684

### Re: Square root of 0

But just try going a little LESS than 0 and find a square root.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #6 2005-07-21 10:10:25

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Square root of 0

Mathematicians were asked this question, to which there is no real answer, and they were vexed.
They do not like to be told that they do not have an answer, so they imagined one.
Hence, the imaginary number i was born.

Also, if you're interested, √i=(1+i)/√2.

Why did the vector cross the road?
It wanted to be normal.

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## #7 2005-07-21 16:23:52

ganesh
Registered: 2005-06-28
Posts: 24,235

### Re: Square root of 0

Hi, I love pi! Welcome to the forum!
Trying to find the square root of 0 using logarithms is not possible
as log 0 is not defnined. This is because any number raised to any number cannot be 0. That includes 0.
The square root, cube root, fourth root etc, of 0 IS 0.
This is because
0² = 0
0³ = 0
0^4 = 0 and so on.
Any nth root of 0 is 0, the only condition being n ≠ 0.
This follows from the fact that
if a^b = c, then bth root of c = a.
The birth of imaginary numbers is, indeed, interesting.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #8 2005-07-21 17:42:08

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Square root of 0

e^(i*pi)=1

Why did the vector cross the road?
It wanted to be normal.

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## #9 2005-07-21 21:31:58

03barojo
Member
Registered: 2005-07-20
Posts: 1

Hello dear.

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## #10 2005-07-21 21:48:31

MathsIsFun
Registered: 2005-01-21
Posts: 7,684

### Re: Square root of 0

Hi hunny.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #11 2005-07-21 23:28:10

ganesh
Registered: 2005-06-28
Posts: 24,235

### Re: Square root of 0

mathsyperson wrote:

e^(i*pi)=1

Of the five numbers considered important in mathematics, this number relates four.
I think this equation was given by Loenard Euler.
This, I think,  is a result of
e^(i*theta) = cos (theta) + i sin(theta)
and
Abraham de Moivre's theorem, according to which
(Cos(theta)+i*sin(theta))^n = cos n(theta) + i*sin n(theta)
which can be written as
e^(n*i*theta) = Cos n(theta) + i*sin n(theta)

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #12 2005-07-22 01:50:20

hdelworth
Member
Registered: 2005-07-22
Posts: 1

### Re: Square root of 0

i have no clue how to work out pie questions could you please explain to me in simple terms how to work out the the pie formula
thanks helen

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## #13 2005-07-22 16:46:51

ganesh
Registered: 2005-06-28
Posts: 24,235

### Re: Square root of 0

Hi Helen,
I don't know what you mean by pie questions and pie formula.
If you mean pi, I shall explain to you.
Pi is a Greek alphabet used to represent the ratio of the circumference of a circle to its diameter, which is always a constant.
Pi is taken as 3.14 or 22/7, as an approximation,
but the actual value of pi is
3.14159265358979323846264338327950288.......it goes on and on.
The area of a circle of radius 'r' is
pi*r²  and its circumference is 2*pi*r
Similarly, the volume of a sphere of radius'r' is
4/3*pi*r³  and its area is 4*pi*r² .
Pi is also an angle of 180 degrees.
Therefore, pi/2 would be 90 degrees and pi/4 45 degrees.
If you have any specific doubt, you can post in this forum.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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thushika
Guest

cool

## #15 2005-07-22 19:06:51

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Square root of 0

ganesh wrote:

Pi is also an angle of 180 degrees.

That's when the angle is in radians. e.g. 180 degrees = pi radians

You can approximate pi like so:

Get a matchstick and measure it. Then get a piece of paper and draw parallel lines on it, so that they are the same distance apart as the length of the match. Then flip the match onto the piece of paper and note whether it crosses a line. Keep doing this until you get bored, but the more times you do it, the better your estimation will be.

You can use your results to approximate pi by knowing that the probability of it landing on a line is 2/pi. There's something for you to do when you're bored!

Why did the vector cross the road?
It wanted to be normal.

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## #16 2005-08-06 21:31:41

dollysaunder
Member
Registered: 2005-08-06
Posts: 3

### Re: Square root of 0

i forgot whta square root is!

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## #17 2005-08-08 00:10:18

ganesh
Registered: 2005-06-28
Posts: 24,235

### Re: Square root of 0

Square root of a number A is a number B which multiplied by itself gives the number A.
eg
square root of 25 = ±5 (that is +5 or -5, because both +5 x +5 = 25 and -5 x -5 = 25)
square root of 2401 = ±49
square root of 65536 = ±256
square root of 0 = 0
square root of 1 = ±1
square root of 2 = 1.4142135623..........................
square root of 10 = 3.1622776601........................
Those decimals appear because 2, 10 etc are NOT perfect squares.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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