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

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

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- May 7th 2011, 06:12 AMdumluckFinding the value of a square root
What would be the quickest method to estimate (i.e to the nearest integer) the value of $\displaystyle 3\sqrt{-89}$?

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, 06:34 AMCaptainBlack
- May 7th 2011, 07:02 AMWilmer
For a really "rough" estimate:

sqrt(100) = 10

sqrt(81) = 9

10 > sqrt(89) > 9 ; get my drift? - May 7th 2011, 07:10 AMdumluck
- May 7th 2011, 07:22 AMdumluck
Ok I think I have it 4.4.4 = 64 5.5.5 = 125 therefore it is between -4 and -5.

- May 7th 2011, 08:20 AMCaptainBlack
- May 7th 2011, 08:37 AMHallsofIvy
The fact that you wrote "$\displaystyle 3\sqrt{-89}$"

**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, $\displaystyle \sqrt[3]{-89}$.

$\displaystyle -4^3= -64$ and $\displaystyle -5^3= -125$ so the cube root of -89 is between -4 and -5.