Perform the indicated operations and/or simplify each expression....

Question

Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. 5/√2

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression seven divided by the squared of three. Were asked to rationalize this. We need to simplify it so that there is no radical in the denominator. Well how do we do that? Well we know that in order for anything to come out of this radical there needs to be two of that factor because there's this unwritten index of two here for are radical. And so we need another square root of three so that we'll have two threes that can come out. But what we multiply the denominator by. We need to multiply the numerator by as well. So that in effect we're multiplying it by one. So let's go ahead and do that multiplication. In the numerator we have seven times the square root of three. And in the denominator we have the square root of three times three. Well we know that the square root of three times three or three squared or nine. The square root of all of that is just three. So our denominators three and our numerator is seven squared of three. There's no simplification that can happen there, nothing can come out of the radic. If we have R seven and R. Three, they don't have any common factors to reduce each other by. So this is our final simplified answer. We look at our answer choices for seven squared of three divided by three. And that matches with answer choice C. Well done. We'll catch you on the next one

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Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. 5/√2

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