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Mathematics 21 Online
OpenStudy (logan13):

What is 3 root of 250? A. 5 3 root of 2 B. 2 3 root of 5 C. 5 3 root of 3 D. 3 3 root of 5

jimthompson5910 (jim_thompson5910):

hint \[\LARGE \sqrt[3]{250}=\sqrt[3]{125*2}\] I'm picking on 125 because 5^3 = 5*5*5 = 125

TheSmartOne (thesmartone):

You were on this questions hours ago, and I gave you the same hint that Jim gave you. Here's a new one: \(\Large\bf \sqrt[3]{x^3} = x\)

OpenStudy (logan13):

i know i closed re posted it i think B

TheSmartOne (thesmartone):

Why do you think it is B? How did you pull out 2 from the cube root? You can only pull out 2 if it was inside the cube root three times, like 2 * 2 * 2.

OpenStudy (logan13):

HMM my second final guess is D

jimthompson5910 (jim_thompson5910):

\[\LARGE \sqrt[3]{250}=\sqrt[3]{125*2}\] \[\LARGE \sqrt[3]{250}=\sqrt[3]{125}*\sqrt[3]{2}\] \[\LARGE \sqrt[3]{250}=\sqrt[3]{5^3}*\sqrt[3]{2}\] I'll let you finish

jimthompson5910 (jim_thompson5910):

I'm using the rule \[\LARGE \sqrt[n]{x*y} = \sqrt[n]{x}*\sqrt[n]{y}\]

OpenStudy (logan13):

I need this done C

OpenStudy (logan13):

@jim_thompson5910

jimthompson5910 (jim_thompson5910):

what is \[\LARGE \sqrt[3]{5^3}\] equal to?

OpenStudy (logan13):

D right?

jimthompson5910 (jim_thompson5910):

please stop randomly guessing

jimthompson5910 (jim_thompson5910):

what is \[\LARGE \sqrt[3]{5^3}\] equal to?

OpenStudy (logan13):

my brain hurts sorry i want this done as quickly as possible

OpenStudy (logan13):

A

jimthompson5910 (jim_thompson5910):

The 3s will cancel \[\LARGE \sqrt[3]{5^3} = \sqrt[{\color{red}{3}}]{5^{{\color{red}{3}}}}\] \[\LARGE \sqrt[3]{5^3} = \sqrt[{\color{red}{\cancel{3}}}]{5^{{\color{red}{\cancel{3}}}}}\] and so does the radical as well

jimthompson5910 (jim_thompson5910):

Which is why \[\LARGE \sqrt[3]{5^3}=5\]

OpenStudy (logan13):

okay so

jimthompson5910 (jim_thompson5910):

\[\LARGE \sqrt[3]{250}=\sqrt[3]{125*2}\] \[\LARGE \sqrt[3]{250}=\sqrt[3]{125}*\sqrt[3]{2}\] \[\LARGE \sqrt[3]{250}=\sqrt[3]{5^3}*\sqrt[3]{2}\] \[\LARGE \sqrt[3]{250}=5*\sqrt[3]{2}\]

OpenStudy (logan13):

but the closet it seams i get to that is B

OpenStudy (logan13):

23.6440219392 @jim_thompson5910

jimthompson5910 (jim_thompson5910):

I already got to the final answer on the last line

OpenStudy (logan13):

Oh XD i thought you wanted me to multiply that oops

jimthompson5910 (jim_thompson5910):

no the teacher wants you to leave it in exact radical form

OpenStudy (logan13):

thanks for the help im already a fan and i meddled you Thank alot man

jimthompson5910 (jim_thompson5910):

you're welcome

OpenStudy (logan13):

i got one more

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