# Thread: Finding the value of a square root

1. ## 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

2. 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

3. For a really "rough" estimate:
sqrt(100) = 10
sqrt(81) = 9
10 > sqrt(89) > 9 ; get my drift?

4. 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?

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

6. 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

7. 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.