Math question
- Thread starter winterhot
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Use a calculator.
Best I can help you with is that 27^0.49 is pretty much the square root of 27 which is probably around 5.2. The 16^0.39 I would guess somewhere between the third and square roots of 16. The square root is 4. The third root is between 2 and 3 which means we're probably dealing with a number close to 3.
Indeed these 2 guesses are pretty close.
Use a calculator 🙂
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i assume you asking this means a calc is not allowed. You can just estimate.
the powers to estimate.
lets look at 16^.39,
This value is approximately between 16^.25 (4th root)
and 16^.5 (square root)
everyone knows 4th root** of 16 is 2, and square of 16 is 4.
Since 16^.39 is in between, estimate that to equal 3.
now that we have that look at 27^.49
take that to ^.5, 27 since its a base, is relatively close to 25, so you know whatever it is you will get a number closer to 25, BECAUSE the next perfect square is 36, which is really far from 27 (base -wise)
so 25^.5 = 5
you have your first estimate to be 3, 2nd estimate to be 5.
so you should look for an answer very close to 8. Probably a LITTLE less since we took OVER estimates.
the powers to estimate.
lets look at 16^.39,
This value is approximately between 16^.25 (4th root)
and 16^.5 (square root)
everyone knows 4th root** of 16 is 2, and square of 16 is 4.
Since 16^.39 is in between, estimate that to equal 3.
now that we have that look at 27^.49
take that to ^.5, 27 since its a base, is relatively close to 25, so you know whatever it is you will get a number closer to 25, BECAUSE the next perfect square is 36, which is really far from 27 (base -wise)
so 25^.5 = 5
you have your first estimate to be 3, 2nd estimate to be 5.
so you should look for an answer very close to 8. Probably a LITTLE less since we took OVER estimates.
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Everyone knows the cube root of 16 is not 2. cube root of 16 is 16^.33, which is a little over 2.5 I think. Just to clarify to the OP.
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you are absolutely right, what i meant was 4th root. sorry about that, thanks for correction Badgerfaithful
Thanks for the information guys. Keep writing these kinds of posts. Atleast we have to know these types of things.
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This might be overanalyzing it but I would do something like this:
16^(.39) + 27^(.49)
= (2^4)^(3*.13) + (3^3)^(.7*.7)
= 2^(4*3*.13) + 3^(3*.7*.7)
= 2^(1.56) + 3^(1.47)
about ~ 2^(3/2) + 3^(3/2)
= 8^(1/2) + 27^(1/2)
= sq.rt(8) + sq.rt(27)
= 2*sq.rt(2) + 3*sq.rt(3)
about ~ 2*1.4 + 3*1.7
= 2.8 + 5.1
= 7.9 (compared to real answer of 7.976)
Might be a little too long-winded and there were 2 approximation steps :\ Meh, just my input 😛
16^(.39) + 27^(.49)
= (2^4)^(3*.13) + (3^3)^(.7*.7)
= 2^(4*3*.13) + 3^(3*.7*.7)
= 2^(1.56) + 3^(1.47)
about ~ 2^(3/2) + 3^(3/2)
= 8^(1/2) + 27^(1/2)
= sq.rt(8) + sq.rt(27)
= 2*sq.rt(2) + 3*sq.rt(3)
about ~ 2*1.4 + 3*1.7
= 2.8 + 5.1
= 7.9 (compared to real answer of 7.976)
Might be a little too long-winded and there were 2 approximation steps :\ Meh, just my input 😛
