Question 1015324
i think you want sqrt(3x^5) * sqrt(18x^6)


in general, sqrt(a) * sqrt(b) is equal to sqrt(a*b)


for example:


sqrt(4) * sqrt(16) = sqrt(4*16) = sqrt(64) = 8


sqrt(4) = 2 and sqrt(16) = 4 so sqrt(4) * sqrt(16) = 2*4 = 8


the answers are the same, so sqrt(4) * sqrt(16) = sqrt(4*16)


so, your solution becomes:


sqrt(3x^5) * sqrt(18x^6) = sqrt(3x^5 * 18x^6) = sqrt(54*x^11) = 3x^5*sqrt(6x)


the simplification process went like this:


sqrt(54*x^11) = sqrt(6*9*x^10*x)


since sqrt(9) = 3, then the expression becomes 3*sqrt(6*x^10*x)


since sqrt(x^10) = x^5, then the expression becomes 3*x^5*sqrt(6x)


why is sqrt(x^10) = x^5?


because (x^5)^2 = x^(5*2) = x^10.


the basic procedure is to remove from under the square root sign, all the perfect squares you can find.


sqrt(9) is a perfect square, so you remove it from under the squareroot sign and place it outside the square root sign because sqrt(9) = 3


sqrt(9) = 3


sqrt(9x) = 3sqrt(x)


the x is not a perfect square so it remains.