In Exercises 65–74, simplify each radical expression and then rat...

Question

In Exercises 65–74, simplify each radical expression and then rationalize the denominator.150a³- √ ----------b⁵

Accepted Answer

Simplify the following expression, then eliminate the radical and the denominator by rationalizing where our expression has a square root of 405, X to the 5th, Divided by Y to the 7th. Now to simplify this, we need to modify all of our terms in a way that we can take the square root of them. So you notice here we have 405. We define factors of four or 5 that allow us to take a square root. We can modify 405 to be 81 multiplied by five X five, we can split up as X squared multiplied by X squared multiplied by X. That would give us X to the fifth. If we were to combine them again. On the denominator, we have Y to the seventh, which is the same as saying Y is the third multiplied by Y to the third multiplied by Y. Now we can simplify by taking the square root on the top. We have the square of 81 which is nine in the square of X squared multiplied by X squared multiplied by X. Since we have two X squared, we'll just take one out take it X squared by itself that is divided by Y to the third because we have two Y to the thirds. All this is multi by what's remaining. And the radical five X is the numerator divided by Y and the Denominator. Now we can go ahead and simplify our radical five x divided by Y. This can be rewritten ss negative nine X squared divided by Y to the third, Multiplied by radical five x divided by radical y multi, everything by radical Y divided by radical Y to get rid of the Y and the denominator, we then get native N squared. What's the pipe by radical by X Y all divided by? What's the third multiplied by Y? Finally, we could simplify it one more time to get negative nine X squared Radical five xy Divided by Y to the 4th. We can't simplify any farther. So then we can determine the answer to our problem corresponds to answer A OK. I hope to help me solve the problem. Thank you for watching. Goodbye.

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In Exercises 65–74, simplify each radical expression and then rationalize the denominator.150a³- √ ----------b⁵

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