Lesson: “Fixing” the Denominator

Comment on “Fixing” the Denominator

I initially took root 25 and turned it into 5, then multiplied the 3 by the 5 to get the answer 2 root 50 over 15. Why is that not correct?
greenlight-admin's picture

Sorry, which question are you referring to?

I think they were referring to rewriting (2*root10)/(3*root5), because I first got the same answer: (2*root50)/15, but as I continued to simply root50, I got the same answer: (2*root2)/3.
greenlight-admin's picture

Thanks kdusold!

So, we're referring to the question at 2:24 in the video.

Once we get to 2√50/15, we can still simplify √50 in the numerator.

√50 = √(25 x 2) = (√25)(√2) = 5√2

So, 2√50/15 = (2)(5√2)/15 = (10√2)/15 = (2√2)/3

Can you multiply conjugate denominators when the root is greater than 2?
greenlight-admin's picture

Yes. The technique works will all denominators.

I dont understand where 10 comes from in 2root25?
greenlight-admin's picture

I believe you're referring to what happens at 5:53 in the video.

We have 2√25

√25 = 5

So, 2√25 = (2)(√25)
= (2)(5)
= 10

Cheers,
Brent

If all the terms in the denominator are negative do you change all terms to positive for it's conjugate?
greenlight-admin's picture

The basic structure remains the same.

1) If we have (some term) + (some other term), then the conjugate is (some term) - (some other term)

2) If we have (some term) - (some other term), then the conjugate is (some term) + (some other term)

So, for example, if we have √3 + 4, then the conjugate is √3 - 4

If we have -√3 - 4, then the conjugate is -√3 + 4

Does that help?

Cheers,
Brent

Is the best approach to the GCF question to try out numbers like everyone did in the replies? https://greprepclub.com/forum/if-c-and-d-are-positive-integers-and-m-is-the-greatest-comm-8618.html
greenlight-admin's picture

Question link: https://greprepclub.com/forum/if-c-and-d-are-positive-integers-and-m-is-...

Yes, testing values definitely is the best/fastest approach for that question.

Cheers,
Brent

around 4:00 in the video the answer to the question equals (15 - 5√2)/7
would this not be simplified to be (10√2)/7 ?
greenlight-admin's picture

15 and 5√2 are not "like terms," so we can't combine them (in the same way that 15 - 5x does not simplify to be 10x.)
IF the expression were 15√2 - 5√2, then it would simplify to be 10√2
However, as it stands we can't simplify 15 - 5√2
For more on this, watch: https://www.greenlighttestprep.com/module/gre-powers-and-roots/video/1042

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