Simplify #sqrt(18a^2)xx4sqrt(3a^2)#?

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Answer 1 · 2017-03-29T09:08:18

#= 12 a^2 sqrt6#

#sqrt(18a^2) * 4 sqrt(3a^2) = 4 sqrt(18a^2 *3a^2)#

#= 4 sqrt(54a^4) = 4 sqrt(9 a^4 * 6)#

#= 4 sqrt(9 a^4) * sqrt 6#

#= 4 * 3a^2 * sqrt 6#

#= 12 a^2 sqrt6#

Answer 2 · 2017-03-29T09:57:06

#12a^2sqrt(6)#

You are looking for squared values. These can be 'taken out' of the root.

Given:#" "sqrt(18a^2)xx4sqrt(3a^2)#

We can 'extract' the #a^2# giving:

#asqrt(18)xx4asqrt(3)#

3 is a prime number so that root can not be changed (at the moment).

Note that #18->2xx9->2xx3^2# giving:

#asqrt(2xx3^2)xx4asqrt(3)#

We can 'extract' the #3^2#

#3asqrt(2)xx4asqrt(3)#

Check the next step out on a calculator. It does work!

Combining the contents of the roots.

#3axx4axxsqrt(2xx3)#

#12a^2sqrt(6)#

Answer 3 · 2017-03-29T09:58:27

#color(red)(12a^2sqrt6#

#sqrt(18a^2)*4sqrt(3a^2)#

#:.=sqrt(2*3*3*a*a) xx 4sqrt(3*a*a)#

#color(red)(Note:#

#:.=color(red)(sqrta*sqrta=a# or #color(red)(sqrt(a*a)=a#

#:.=3asqrt2 xx 4*asqrt3#

#:.=12a^2sqrt2 xx sqrt3#

#:.=12a^2sqrt(2*3)#

#:.color(red)(=12a^2sqrt6#