SOLUTION: multiply and simplify sqroot 12a^2b multiply sqroot15ab^2

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Question 275568: multiply and simplify
sqroot 12a^2b multiply sqroot15ab^2
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28+12a%5E2b%29%2A+sqrt%2815ab%5E2%29
One of the properties of radicals is: root%28a%2C+p%29%2Aroot%28a%2C+q%29+=+root%28a%2C+p%2Aq%29
We will ue this property in both "directions". We will start by using it to multiply the two square roots into one:
sqrt%28+12a%5E2b%2A15ab%5E2%29
Simplifying the radicand (the expression inside a radical) we get:
sqrt%28+180a%5E3b%5E3%29
The last stage is to simplify the square root. This involves finding factors of the radicand that are perfect squares:
sqrt%28+36%2A5%2Aa%5E2%2Aa%2Ab%5E2%2Ab%29
Now we will use the property in the other direction to separate the factors into their own square roots:
sqrt%28+36%29%2Asqrt%285%29%2Asqrt%28a%5E2%29%2Asqrt%28a%29%2Asqrt%28b%5E2%29%2Asqrt%28b%29
Simplifying the square roots of the perfect squares we get:
6%2Asqrt%285%29%2Aa%2Asqrt%28a%29%2Ab%2Asqrt%28b%29
And finally we'll use the Commutative Property of Multiplication to rearrange the factors and our property of radcials to re-combine all the remaining square roots:
6ab%2Asqrt%285ab%29