How do you calculate this? Is there a formula for this?
16^0.39 +27^0.49 = ?
Thanks in advance!
16^0.39 +27^0.49 = ?
Thanks in advance!
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
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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 😛
