How do you approximate this fraction power?

👨🏻‍🏫 學術台數學

itguru5354

2009-11-06 10:46 pm

4^(1/3) I know it is 2^(2/3) Now, how do you approximate this the value of 2^(2/3)? Any rule to remember? Thanks

更新1:

No, can't use a calculator. That's the rule =(

更新2:

Thanks for the tip. 2^(2/3) = 2^(1/3) + 2^(1/3) Yes, 2^(1/3) is a little less than root(2).

更新3:

Thanks for the tip. 2^(2/3) = 2^(1/3) + 2^(1/3) Yes, 2^(1/3) is a little less than root(2).

更新4:

I mean 2^(1/3) * 2^(1/3)

回答 (4)

[匿名]

2009-11-06 10:56 pm

✔ 最佳答案

I believe that 2^(1/3) is about 1.26. So 1.25² would be

1.26 + .25(1.26) + 1.25 + 0.32 = 1.57

The calculator gives 1.59 as the correct answer rounded off to 2 places

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[匿名]

2009-11-07 6:52 am

just plug it in a calculator and round to whatever digit of precision that you want. 2^(2/3) = ( ( 2^(1/3) ) )^2 so take the cube root of 2 in calculator then square that value and round to whatever digit of precision to approximate this value.

參考: my head

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[匿名]

2009-11-07 6:50 am

use a calculator

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[匿名]

2009-11-07 6:50 am

2^(2/3) = cuberoot(2^2).

A fractional exponent is the bottom number root of the top number squared. You can approximate this as closer to 1 than 2.

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