Simplify? #sqrt8 xx sqrt(48^3)#

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Answer 1 · 2017-10-20T01:30:22

#sqrt8 xx sqrt(48^3)=384sqrt6#

#sqrt8 xx sqrt(48^3)#

Because both terms are under a square root sign, we can combine them:

#sqrt(8xx48^3)#

Rather than doing the cube of 48 first, let's see that #8=2^3#, and so we can combine again:

#sqrt(2^3xx48^3)=sqrt(96^3)=96^(3/2)#

I'll go ahead and cube now, then work on the square root after:

#sqrt884736=sqrt(16384xx54)#

(I kept dividing by 4 to find the 16384).

Note that #2^14=16384#, and so #sqrt(2^14)=2^7=128#. Also, #54=9xx6# and so #sqrt54=3sqrt6#

Putting it together, we get:

#sqrt884736=sqrt(16384xx54)=128xx3xxsqrt6=384sqrt6#