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OpenStudy (anonymous):

Multiplying radicals 5√6x2x√6 (addition problem)

OpenStudy (anonymous):

@jim_thompson5910

OpenStudy (anonymous):

Please help

jimthompson5910 (jim_thompson5910):

so you want to multiply \(\large 5\sqrt{6}\) with \(\large 2\sqrt{6}\) right?

OpenStudy (anonymous):

Correct

jimthompson5910 (jim_thompson5910):

ok what you do is multiply the coefficients to get: 5*2 = 10 then you multiply the terms inside the square root: 6*6 = 36

jimthompson5910 (jim_thompson5910):

so that will turn \(\large 5\sqrt{6}*2\sqrt{6}\) into \(\large 10\sqrt{36}\)

jimthompson5910 (jim_thompson5910):

from here, you take the square root of 36 to get 6

jimthompson5910 (jim_thompson5910):

so \(\large 10\sqrt{36}\) turns into \(\large 10*6\) I'm sure you see how to finish up

jimthompson5910 (jim_thompson5910):

so what's the final answer?

OpenStudy (anonymous):

60

jimthompson5910 (jim_thompson5910):

yep, so \(\large 5\sqrt{6}*2\sqrt{6} = 60\)

OpenStudy (anonymous):

its 2x

jimthompson5910 (jim_thompson5910):

oh so not 2 times the square root of 6?

jimthompson5910 (jim_thompson5910):

but 2x times the square root of 6?

OpenStudy (anonymous):

5√6 x 2x√6

jimthompson5910 (jim_thompson5910):

ok let me redo use * to mean multiplication since x is a variable

jimthompson5910 (jim_thompson5910):

\(\Large 5\sqrt{6}*2x\sqrt{6}\) \(\Large 5*2x\sqrt{6*6}\) \(\Large 10x\sqrt{36}\) \(\Large 10x*6\) \(\Large 10*6x\) \(\Large 60x\) So, \(\Large 5\sqrt{6}*2x\sqrt{6} = 60x\)

OpenStudy (anonymous):

Thanks

jimthompson5910 (jim_thompson5910):

yw

OpenStudy (anonymous):

i have another one

jimthompson5910 (jim_thompson5910):

ok one more

OpenStudy (anonymous):

(4√3)(-5√21)

jimthompson5910 (jim_thompson5910):

no x variables this time?

OpenStudy (anonymous):

no

jimthompson5910 (jim_thompson5910):

ok one sec

jimthompson5910 (jim_thompson5910):

\(\Large (4\sqrt{3})*(-5\sqrt{21})\) \(\Large (4)*(-5)*\sqrt{3*21}\) \(\Large -20*\sqrt{63}\) \(\Large -20*\sqrt{9*7}\) \(\Large -20*\sqrt{9}*\sqrt{7}\) \(\Large -20*3*\sqrt{7}\) \(\Large -60*\sqrt{7}\) In the end, \(\Large (4\sqrt{3})*(-5\sqrt{21}) = -60*\sqrt{7}\)

OpenStudy (anonymous):

thanks

jimthompson5910 (jim_thompson5910):

np

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