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Anna11 [10]
3 years ago
14

Why is the square root of a perfect square always rational?

Mathematics
1 answer:
vova2212 [387]3 years ago
6 0
Basically because you can break any square root of non-perfect square into the square root of prime factors.
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Pls help ASAP!! 15 points?
GalinKa [24]

Answer:

4 gte g

Step-by-step explanation:

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Which set of line segments could create a right triangle?
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Waht is the area of a parallelogram wiht a base of 20cm and a height of 9cm?
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How to get from 92 to 280 in 4 jumps. This is supposed to be an exponential equation. You have to multiply the same number every
bogdanovich [222]
The exponential function is
f(x)=ab^x, where b is the base, the number to multiply every time x is increased by 1.

If f(x)=92, f(x+4)=280, then
f(x+4)/f(x) = 280/92 = ab^(x+4)/(ab^x) = b^4
to find the base b,
b^4=(280/92)
b=(280/92)^(1/4)    ..... fourth root, or take square-root twice
=3.4035^(1/4)
=1.3208  (accurate to 4 places of decimal).

Edit: 92*1.3208^4 gives 279.9858  (missing little bit because of accuracy).
A slightly better accuracy would be
base = 1.320816698856163
and 92*1.320816698856163^4 would still be 279.9999999999993, but VERY close to 280.  
So it all depends on the accuracy you need.
If you need more accuracy, please tell me how many accurate digits you'd like the results.
Here it is:
base = 1.320816698856163713875997666455513013800337299231824403890097792042432005288739246325005446716740
and if you multiply together
92*base^4, you will get 280 accurate to at least 90 digits after the decimal.  
I think that should be sufficient for what you need.  Recall that these calculations cannot be done or verified on a 10 or 12 digit calculator.

Well, to please you, I have calculated it to 500 digits, don't think that's going to be of much practical use for anybody.  
By the way, that's as far as I will do this evening.  My eyes are almost closing!

base=1.3208166988561637138759976664555130138003372992318244038900977920424320052887392463250054467167408005624428737585147309981331510076693180633495574937759374668399829195521733208637815593771220504215429477168159456265024711237470736388371979840461777898466419772297172931568429339640964205400234392902077320257671263508487367942846685479533507498695981037274512050120058009244868634949261015429944340565311559486391625531554216085859773912355361847787636892603324966350039688974359584811585283183726532
8 0
3 years ago
Write the exponent for the expression.2.78<br><br> The exponent for the expression is ___
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Answer:

The exponent for the expression is -8

Step-by-step explanation:

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