Question

Write the following expression as a decimal rounded to two decimal places.

Answer 1

\[\sqrt[3]{118}\]

Answer 2

@whpalmer4 can you help me with this one please

Answer 3

@ganeshie8 can you help me with this one please

Answer 4

To round it, just take the first two digits after the decimal point, then to work out if you round the second up or down you need to look at the third digit, if it is 5 or above, you round the second digit up, if it's four or below you round down..

e.g. 9.458243
would be 9.46 to two decimal places

So if cube root '118' is 4.90486
How would you round it to 2dp?

Answer 5

it would be 4.90 but how do you get the 4.90486

Answer 6

Do you have to work it out by hand?

Answer 7

no I dont but I would like to understand how to do it

Answer 8

Do you have a calculator that does logarithms or y^x?

Answer 9

I have the basic calculator that comes on the computer

Answer 10

well, you can use http://web2.0calc.com/ which even has a cube root button...

Answer 11

I figured it out on the calculator, I changed the settings on it

Answer 12

ah, there was a mode for scientific, I take it?

Answer 13

yes

Answer 14

is there a way that I could figure it out by hand

Answer 15

Okay I'll try and explain
So if you want to find the cube root by hand here is a good estimation

Look at your number [ie 118]
and think of what numbers cubed could give you a similar number
[ie 4^3=64, but 5^3 is too big, so you would know that it's going to be 4.xxxxxxx]

Then there is like a little algorithm for it
but it's quite difficult to explain in theory, i'll give you the link for it, and maybe some practice with numbers it might be clearer

http://www.wikihow.com/Calculate-Cube-Root-by-Hand

Hope this helps :)

Answer 16

oh, painfully...you could guess that say 5 was about the right answer (5^3=125) and start multiplying 5*5*5 = 125, little too big, try 4.5*4.5*4.5 = 91.125 too small, try splitting the difference, 4.75*4.75*4.75 = 107.172 still too small, 4.875*4.875*4.875 = 115.857 just a bit too small, try 4.9375*4.9375*4.9375=120.371 just a bit too big, etc.

Answer 17

I've never met anyone who uses the methods for directly computing cube roots and even square roots often enough to reliably remember and execute them :-)

Answer 18

ok I understand now and I want to thank both of you for helping me out. I am sure I would never use this in the future but I am sure it will be on my final exam so I wanted to make sure that I understood it.

Answer 19

I completely agree, you will only be given simple integers to cube root by hand, otherwise I'm sure you would have access to a calculator, too much time wasting :)

It's a good thing to understand, but in practice there's not much point in trying to remember the process!

Answer 20

If you've got log tables, you could take the log of 118, divide by 3, take the anti-log.

Answer 21

@cahayes9498 good attitude to have :) and no problem!

Answer 22

If you're bored some day, work out how you could approximate square roots by thinking of the number as a square, then adding rows to get closer.

For example, computing the square root of 10, well, that's going to be

\[(3+x)(3+x) = 9+6x+x^2 = 10\]where \(x\) is the part to the right of the decimal point. If you assume that \(x^2\) is small because \(x < 1\), then \(x\approx \frac{1}{6}\) which means \(\sqrt{10}\approx 3+0.1666..\) which compares well with the actual value of \(\sqrt{10} \approx 3.16228\)
You can do the same for cube roots, except now you are thinking of cubes instead of squares.