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Squaring / cubing decimals

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by sophadel » Mon Jan 04, 2010 3:22 am
Hello!

I always get these types of questions wrong:

What is the value of sq root(cube root(0.000064))

I know the answer is 0.2 but I never seem to get the right number of decimal places (e.g. when I did this question I actually got 0.02). can someone explain a foolproof way of doing this?

Thanks :)
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by sadullaevd » Mon Jan 04, 2010 5:29 am
here is my approach:

sqr(cube root(0.000064))=sqr(cube root(64/1000000))=sqr(cube root(4^3/(10^2)^3 ))= sqr(4/10^2)=2/10=0.2

here it looks horrible/nasty, but if u try it on a paper , i'm sure it'll get much clearer to understand.

overall, the main point is , change decimal to fraction, this way u can see real numbers without zeros and decimal marks,

for me its easier to find square root of (1/4) than of (o.25)

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by papgust » Mon Jan 04, 2010 6:08 pm
You could do this way too.

sqr(cube root(0.000064))

sqr(cube root(64 * 10^-6))

Take cube root for both 64 and 10^-6,

sqr(4 * 10^-2)

Now take sqr root for both 4 and 10^-2,

2 * 10^-1

=0.2
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by Energie411 » Mon Oct 08, 2012 7:41 pm
*You can ignore the decimals and solve (then place correct decimals)

For the square root of the cube root of .000064 (6 decimal places):

First do the cube root of 64 which equals 4
-adjust decimal point 2 places to the left so you get .04 (since you divide the number of decimals by 3 for cube roots--6/3=2)

Second do the square root of 4 which equals 2
-adjust decimal point 1 place to the left so you get .2 (since you divide the number of decimals by 2 for square roots--2/2=1)
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by Whitney Garner » Mon Oct 08, 2012 7:55 pm
sophadel wrote:Hello!

I always get these types of questions wrong:

What is the value of sq root(cube root(0.000064))

I know the answer is 0.2 but I never seem to get the right number of decimal places (e.g. when I did this question I actually got 0.02). can someone explain a foolproof way of doing this?

Thanks :)
Hi sophadel!

I'm TOTALLY with you on the decimals. I mean, decimals in powers and roots are TERRIBLE. So why not make life a million times easier and covert to a fraction:

.000064 would be 64 over a 1 with 6 zeros (for the 6 decimal places), or a 10 to the power of 6 (for the 6 decimal places).

Image
**Note that I used some helpful rules like the fact that I can break up a root over multiplication or that a root is the same as a fractional exponent**

Hope this helps!
:)
Whit
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Math is a lot like love - a simple idea that can easily get complicated :heart-eyes:
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