How do you simplify #sqrt(6ab) * sqrt(3a)#?

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Answer 1 · 2016-06-09T11:26:47

Remember that #sqrtAxxsqrtB=sqrt(AxxB)#

#=sqrt(6abxx3a)=sqrt(18a^2b)=sqrt(2xx3^2xxa^2xxb)#

We can now take out the squares to leave:

#=sqrt(3^2)xxsqrt(a^2)xxsqrt(2xxb)= 3asqrt(2b)#

Answer 2 · 2016-06-09T11:31:54

#3asqrt(2b)#

We can write the given expression as:

#sqrt(6abxx3a)#

#=sqrt(2xx3xxaxxbxx3xxa)#

We can re-arrange the expression as:

#=sqrt(2xxcolor(red)(3xx3)xxbxxcolor(blue)(axxa))#

We know that #sqrt(3xx3)=3" and "sqrt(axxa)=a#

Therefore, we can take #3# and #a# out of the square root sign and the other terms remain under the square root:

#=3asqrt(2b)#