SOLUTION: ((5x)((3y^2)/2)^(1/2))-((3y)((8x^2)/3)^(1/2))+((2)((3x^2y^2)/2)^(1/2))

Question 624840: ((5x)((3y^2)/2)^(1/2))-((3y)((8x^2)/3)^(1/2))+((2)((3x^2y^2)/2)^(1/2))
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Since exponents of 1/2 mean the same thing as square roots, I am going to rewrite the expression with square roots:

Next we will simplify each square root. Part of simplifying square roots is rationalizing the denominators. There are a variety of ways to go about doing this. I like to start by making each denominator a perfect square:

which leads to:

Next we use the property of radicals to split each square root:

Because of our earlier work, each denominator will simplify:

Next we simplify the square roots in the numerators. Each one happens to have one or more prefect square factors (which I like to put first using the Commutative Property of Multiplication):

Now we use another property of radicals, , to split the square roots so that each perfect square factor is in its own square root:

Each of the square roots of the perfect squares simplify:

which simplifies further to:

The last two fractions reduce:

And last of all, these are all like terms! They are all terms. So we can add/subtract them. Just add/subtract the coefficients. To see this more easily, I'm going to rewrite the first and third terms so we can see the coefficient we should add:

which simplifies to:

since
So

simplifies to

or, if you prefer the 1/2 exponents:

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