In Exercises 75–92, rationalize each denominator. Simplify, if po...

Question

In Exercises 75–92, rationalize each denominator. Simplify, if possible.

17
----------
√10 - 2

Accepted Answer

Rationalize the denominator of the following and express it in its simplest form where we have 11 divided by the square root of -3. To rationalize this, we wanna get rid of the radical and the denominator to do that, we will multiply our denominator by square to plus three. So we'll change our sign in the middle Does help us make use of the difference of two squares. Now, because we're multiplying the sun as a nominator, we also have to do the same in the numerator for this to work. Now, we can go ahead and multiply over our chart. On the top, we have 11 multiplied by the squared of 21 plus three divided by, on the bottom, we can use the foil Squared of 21 multiplied by squared of because there's 21 Square of 21 multiplied by three, gives us three squares of 21, negative three multiplied by the squared of 21 gives us negative three squared to 21 finally negative three multiplied by three gives us negative nine. We can simplify it even further 11 multiplied by the square of plus three Bottom will just simplify to 12th. We can not distribute par 11. You will get 11 spirits of 21 Plus divided by 12. Now, we can go even further and split up the terms of our numerator To get 11 periods of 21 divided by 12 plus 33, divided by 12. We can't simplify any further. So our answer corresponds to answer B OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 75–92, rationalize each denominator. Simplify, if possible. 17 ---------- √10 - 2

Key Concepts

Rationalizing the Denominator

Simplifying Radicals

Properties of Exponents

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