SOLUTION: Multiply and simplify. Assume that all variables represent nonnegative numbers
(-5sqrt6)(2sqrt3)
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Question 350866: Multiply and simplify. Assume that all variables represent nonnegative numbers
(-5sqrt6)(2sqrt3)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Since this expression is all multiplication and since multiplication is commutative and associative, we change change the grouping and/or order in any way we choose. So I am going to rearrage the factors so that the coefficients are together and grouped and the square roots are together and grouped:
The first part is easy to multiply. To multiply the square roots we need to know a basic property of radicals: . We can use this to multiply square roots. Now we have:
which simplifies to
We are almost done. Just like you should reduce/simplify answers that are fractions, you also should simplify square roots. To simplify a square root you look for perfect square factors in the radicand (the expression inside the square root). Since 18 has a perfect square factor, 18 = 9*2, we can simplify, using the property we used eariler:
Since :
which simplifies to:
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