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

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

0

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

0 to any power is 0

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,647

Could be 0.

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

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

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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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,647

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

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.

So in answer to your question: √(-x)=(√x)i.

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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 22,987

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.

I had read somewhere that imaginary numbers have practical applications too!

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

e^(i*pi)=1

Why did the vector cross the road?

It wanted to be normal.

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

Hello dear.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,647

Hi hunny.

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

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 22,987

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

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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 22,987

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

thanks for answering

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

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

i forgot whta square root is!

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 22,987

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.

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

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