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.
__ ___
√8x ⋅ √10y

Accepted Answer

For multiplication. And 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 12 P multiplied by the square root of 14 Q. Possible answers being for route 21 P Q four, route 42 P Q two P Q route 42 route 42 P Q. No, we can rewrite our multiplication of radicals. If we have the square root of a multiplied by the square root of B, this can be rewritten as a square root of a multiplied by B under the same radical. So in other words, we can take square the 12 P multiplied by the square of the 14 Q and rewrite it 12 P multiplied by 14 Q under the radical like so factor my 12 and my 14 to get two multi by six P by 14 2 multiplied by seven Q. This gives us the square root of four multiplied by P Q. Now the only thing that has a perfect square with the radical is four. So we can take the square root of four to get two square roots of P Q, we can't simplify any further. It's our answer corresponds with answer D 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. _ √8x ⋅ √10y