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Mathematics 18 Online
OpenStudy (anonymous):

171/3 is the same as the cube root of 17. True or False

OpenStudy (anonymous):

False

OpenStudy (whpalmer4):

If 171/3 * 171/3 * 171/3 = 17, then the answer is true

OpenStudy (whpalmer4):

Cube root of a number is the number that when multiplied by itself 2 times gives you the first number. For example, 2 is the cube root of 8, because 2*2*2 = 8. 3 is the cube root of 27, because 3*3*3 = 27.

OpenStudy (anonymous):

Yes to all that whpalmer4 laid out for you. And besides, the cube root of 17 is 2.5712815906582353554531872087397

OpenStudy (anonymous):

\[\frac{ 171 }{ 3 }=57\] \[\sqrt[3]{17}\approx \pm2.57 \]

OpenStudy (anonymous):

wait this question was wrong ... its |dw:1370573807036:dw|

OpenStudy (anonymous):

Yes it is, just as 7^(1/2) is the same as sqrt(7)

OpenStudy (anonymous):

Er scratch that. Sorry, it isn't the same as the cube root of 17, it IS the same as the cube root of 7!

OpenStudy (anonymous):

so its false ?

OpenStudy (whpalmer4):

\[7^{1/3} \ne \sqrt[3]{17} \]

OpenStudy (anonymous):

Yes, it it false. Providing that the question was "is 171/3 the same as the cube root of 7.

OpenStudy (anonymous):

no, cube root of 17 not 7

OpenStudy (whpalmer4):

Maybe this will clear things up: \[\sqrt[3]{x} = x^{1/3}\]

OpenStudy (whpalmer4):

cube root is the same as raising to the 1/3 power

OpenStudy (whpalmer4):

square root is the same as raising to the 1/2 power

OpenStudy (whpalmer4):

\[\sqrt[3]{17} = 17^{1/3}\]

OpenStudy (anonymous):

No, I think you've been writing it wrong all down the line. You first wrote 171/3 then you wrote \[7^{1/3}\] And I think what you MEAN is \[17^{1/3}\] And yes, \[17^{1/3} = \sqrt[3]{17}\]

OpenStudy (whpalmer4):

it really, really makes life much simpler if you tell us the problem accurately :-)

OpenStudy (anonymous):

its 7 ^ 1/3

OpenStudy (whpalmer4):

The takeaway here is that a cube root (square root sign with a 3 in the crook) is the same as raising the number to the 1/3 power. Use that knowledge to answer your problem, whatever it is.

OpenStudy (anonymous):

It's been said before, but explicitly, x to a 1/n power is the same thing as the nth root of x.

OpenStudy (anonymous):

okay so i did it and its false :) right

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