In Exercises 39–64, rationalize each denominator.1-----³√3

Question

Accepted Answer

Hello, everyone. We've been asked to eliminate the radical in the denominator by rationalizing the expression we are given is one over the cubed route of 11. We have four answer choices, all of which have a cube root in them and three of the four of them are fractions still. So let's see how this works out. I'm gonna rewrite one over the cube root of 11. And then I recall that to rationalize a denominator, I wanna make it. So the exponent and the index in the denominator match so that they cancel out. So I'm gonna multiply both the numerator and the denominator by a value that will make the denominator cancel out. Since we're working with a Q group, what we multiply our numerator and denominator by will be a cubed group. What's under the cube root is an 11, we wanna have an exponent of three on this 11. The easiest way to do that will be to multiply this 11 to the first power by 11 squared. Because recall when you multiply bases, you add the exponents. So 11 multiplied by 11 squared should give us 11 to the third power or 11 cubed So we are multiplying both the numerator and the denominator by the cubed root of 11 squared. In doing this multiplying across the top one multiplied by the cubed root of 11 squared will give me the cubed root of 11 squared. In my denominator cubed root multiplied by a cubed root will still result in a cubed roop 11 rays to the first power multiplied by 11 rays to the second power would give us 11 rays to the third power or 11 cubed. I'm gonna simplify this and clean it up a little bit. So the cube root of 11 squared can be rewritten as the cubed root of 121. And in the denominator, the cube route of 11 cubed, the cube and the cube root will cancel out leaving us with 11 in our denominator looking at it quickly to see. Is there a perfect cube that I can factor out of 121 to simplify this any further? Um It does not appear that there is. So this would be our answer, the cubed route of 121/11. And that's answer choice. D have a nice day.

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In Exercises 39–64, rationalize each denominator.1-----³√3

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