# Finding the value of a square root

• May 7th 2011, 07:12 AM
dumluck
Finding the value of a square root
What would be the quickest method to estimate (i.e to the nearest integer) the value of $3\sqrt{-89}$?

If 89 has a factor of 3 it wouldn't be too bad but given that its a prime this question seems a little difficult.

thx
• May 7th 2011, 07:34 AM
CaptainBlack
Quote:

Originally Posted by dumluck
What would be the quickest method to estimate (i.e to the nearest integer) the value of $3\sqrt{-89}$?

If 89 has a factor of 3 it wouldn't be too bad but given that its a prime this question seems a little difficult.

thx

$3 \sqrt{-89}=3i \sqrt{89}=-3i \sqrt{10^2-11}$

............. $=- 30 i \sqrt{1+11/100} \approx 30 i (1-(11/100)(1/2)+..)$

CB
• May 7th 2011, 08:02 AM
Wilmer
For a really "rough" estimate:
sqrt(100) = 10
sqrt(81) = 9
10 > sqrt(89) > 9 ; get my drift?
• May 7th 2011, 08:10 AM
dumluck
Quote:

Originally Posted by Wilmer
For a really "rough" estimate:
sqrt(100) = 10
sqrt(81) = 9
10 > sqrt(89) > 9 ; get my drift?

Thanks Wilmer, that's the level I want to be at. However the answer is between -4 and -5?
• May 7th 2011, 08:22 AM
dumluck
Ok I think I have it 4.4.4 = 64 5.5.5 = 125 therefore it is between -4 and -5.
• May 7th 2011, 09:20 AM
CaptainBlack
Quote:

Originally Posted by dumluck
Ok I think I have it 4.4.4 = 64 5.5.5 = 125 therefore it is between -4 and -5.

I'm sorry but it is not between any real numbers it is imaginary. Alternatively you have posted something other than what you think you have.

CB
• May 7th 2011, 09:37 AM
HallsofIvy
Quote:

Originally Posted by dumluck
Thanks Wilmer, that's the level I want to be at. However the answer is between -4 and -5?

The fact that you wrote " $3\sqrt{-89}$" and titled this "Finding the value of a square root" made it very difficult for people to figure out that you really wanted the cube root, $\sqrt[3]{-89}$.
$-4^3= -64$ and $-5^3= -125$ so the cube root of -89 is between -4 and -5.