rationalize

[blndchic0822]

The problem is:

1
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1 + squareroot of 3 - squareroot of 5

I know that you are supposed to multiply the top and bottom by the bottom with opposite signs to rationalize those square roots; however, i've never had to do that with more than two terms on the bottom so i am confused how to get to the answer of...

7 + 3squareroot of 3 + squareroot of 5 + 2squareroot of 15
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11

everything i have tried doesnt seem to work because it doesnt result in that answer. please help.

 

[mmm4444bot]

I know that you are supposed to multiply the top and bottom by the [conjugate of the bottom] to rationalize those square roots; however, i've never had to do that with more than two terms on the bottom so i am confused

You need to multiply twice!

Think of sqrt(3) - sqrt(5) as a constant. In other words, think of that expression as a single number.

The bottom is: 1 + [sqrt(3) - sqrt(5)].

The conjugate is: 1 - [sqrt(3) - sqrt(5)].

So, on the bottom, you need to multiply and simplify the following expression.

(1 + [sqrt(3) - sqrt(5)]) * (1 - [sqrt(3) - sqrt(5)])

Let's see. I can clean this up a bit.

[1 + sqrt(3) - sqrt(5)] * [1 - sqrt(3) + sqrt(5)]

After multiplying the top by the conjugate as well, you should arrive at the following.

[1 - sqrt(3) + sqrt(5)]/[2*sqrt(15) - 7]

Now, carry out the same process again, to rationalize the new bottom.

On the top, it is: [2*sqrt(5) + 7] * [1 - sqrt(3) + sqrt(5)]

On the bottom, it is: [2*sqrt(5) - 7] * [2*sqrt(5) + 7]

Then, simplify the results.