In Exercises 61–82, multiply and simplify. Assume that all variab...

Question

In Exercises 61–82, multiply and simplify. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers.
___ _____
√5xy ⋅ √10xy²

Accepted Answer

Perform multiplication in the given expression. Assume all variables represent positive real numbers and no negative quantities of the radical haven't even exponent. We have the square root of three M N multiplied by the square root of six M N squared. Possible answers three M N route two N M N, route six N three, route two N and M N route two N, no. Our multi location can be rewritten if we know a property route a multiplied by route B is the same thing as saying route A multiplied by B under the same radical. So if we're going to rewrite this, we have the square root of three M N multiplied by six M N squared. In the same radical, we can now simplify to 18 M squared in race to the third. Now we want to take the square root of everything, but we don't have the perfect squares. We need to take the square root. Let's try and form a perfect square out of our remaining terms. 18 can be rewritten as nine multiplied by two. And then the third can be written as N squared multiplied by N which could be further changed. To nine M squared N squared all multiplied by two in not nine in and squared N squared that we can take the square root of you'll get squared of nine, which is three squared of M squared, which is M and A squared of N squared, which is N all multiplied by the square root of two N squared of two N does not have a perfect square. So we can go ahead and say our answer three M N root two N corresponds to answer A OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 61–82, multiply and simplify. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. _ ___ √5xy ⋅ √10xy²