How do you multiply #sqrt(2x^6) *sqrt(6x^4)#?
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It is
#sqrt(2x^6)*sqrt(6x^4)=sqrt(12x^10)=2*sqrt3*absx^5#
#sqrt(2*x^6) * sqrt(6*x^4) = 3.464*x^5#
There are 2 basic approaches available.
1st Approach
Do the square roots first.
#sqrt(2*x^6) * sqrt(6*x^4) = (1.414*x^3) * (2.449*x^2)#
#sqrt(2*x^6) * sqrt(6*x^4) = 3.464*x^(3+2) = 3.464*x^5#
2nd Approach
Combine the 2 radicals first.
#sqrt(2*x^6) * sqrt(6*x^4) = sqrt(2*6*x^(6+4)#
#sqrt(2*x^6) * sqrt(6*x^4) = sqrt(12*x^10) = 3.464*x^5#
I hope this helps,
Steve
With any problem involving the multiplication of two square roots you can use the property #sqrtx times sqrty = sqrt(xy)#
Since a square root is equivalent to #x^{1/2}# we can use the exponential laws for square roots.
#a^xb^x=(ab)^x# --> #sqrtx times sqrty = sqrt(xy)#
#sqrt(2x^6) times sqrt(6x^4)=sqrt(2x^6 times 6x^4) = sqrt(12x^(10))#
#sqrt(12x^10)# can be simplified to #x^5 times sqrt(12)# since #sqrt(x^10) = x^5#
You could also break out a 2 by dividing the inside by 4 (since #sqrt4 =2#) giving you #2x^5sqrt3#
