SOLUTION: Hello Help I hope I got the right sign looks like a check mark, trying to multiply and simplify and show my work please. √3x^5√ 18x^6 Thanks Betty

Algebra ->  Graphs -> SOLUTION: Hello Help I hope I got the right sign looks like a check mark, trying to multiply and simplify and show my work please. √3x^5√ 18x^6 Thanks Betty      Log On


   

Question 1015324: Hello
Help I hope I got the right sign looks like a check mark, trying to multiply and simplify and show my work please.
√3x^5√ 18x^6
Thanks Betty
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20849) About Me  (Show Source):
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.