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. √2/3x

Accepted Answer

Welcome back. I am so glad you're here. We are given the square root of in our numerator. We have five over in our denominator we have seven X. We need to simplify this and ensure that our answer doesn't have a radical in our denominator. No radicals in the denominator allowed. Alright well we recall from previous lessons that when we're taking the square root of a fraction due to the quotient rule of radicals, we can take the square root of the numerator. So the square to five over the square root of the denominator. So the square root of seven X. And now we can work on rationalizing this. Getting that a radical out of our denominator. So how do we do that? Well there needs to be two of any factor inside of our radical there due to this invisible index of two in order for it to get outside of the radical. So there's a seven that's one factor and there's an ex that's another factor. They each need another of themselves. So we can multiply this by the square root of seven X. Then there will be two sevens and two exes. But what we do to the denominator, we need to do to the numerator as well. So that in effect we're multiplying this whole thing times one. So now Multiplying in our numerator, we have the square root of five times 7 x. In our denominator we have the square root of seven X. Times seven x. And we can simplify this. Well we have 2/7 here those will get to come out. We have two exes here. Those will get to come out and when they come out they are just a seven X. In our denominator. Great. Now in our numerator we can multiply our five times are seven. So we're still under the radical here. five times 7 is 35. And then our X. There aren't enough factors of anything in the numerator in order for them to come outside of the radical. So they're just going to remain the square root of 35 X. In the numerator. And the denominator is thrilled. It's just a seven X. So this is as simplified as this one gets. We look at our answer choices for the square root of 35 X. Divided by seven X. And that matches with answer choice B. 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. √2/3x

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