SOLUTION: Please Simplify. sqrt( 16x^7y^5 ) + 9x^2 sqrt( x^3y^5 )

SOLUTION: Please Simplify. sqrt( 16x^7y^5 ) + 9x^2 sqrt( x^3y^5 ) - 3xy sqrt( x^5y^3 )

Question 374545: Please Simplify.
sqrt( 16x^7y^5 ) + 9x^2 sqrt( x^3y^5 ) - 3xy sqrt( x^5y^3 )
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

These are not like terms. So they cannot be added or subtracted as they are. But the square roots can be simplified (because they each have one or more perfect square factors:

I find it helps to use the Commutative Property to rearrange the factors so that all the perfect squares are together (in the front):

Next we can use a property of radicals, , to separate all the perfect square factors into their own square roots:

Each of the square roots with a perfect square radicand (The expression within a radical is called the radicand.) can be simplified:

Simplifying the products in front of the square roots we get:

The square roots are now fully simplified. And now we find that the terms are like terms! (Each term has the exact same square root and outside the square root, each variable has exactly the same exponents.) So we can now add and subtract:

This is the fully simplified expression.
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