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Forgive me if this is a juvenile question, but can someone explain the leap made from the canceling of the "3's" to the singular "1" preceding the root 11 in the answer:
The expression \(\frac{ 3+3 root 11}{ 3 }\)
The solution is: 1+ root 11
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Sometimes, the best of us tend to get entangled in understanding a step that may be simple. So, it’s okay, do not feel that it’s a juvenile question. All of us need help at some point in time.
The square root symbol is not visible in the expression that you have posted. As such, I’m assuming that you posted this: \(\frac{(3 + 3 √11) }{ 3}\)
Do you observe that the number 3 is common to both terms in the numerator? IF yes, can we take this 3 as a common factor? Yes, we can.
So, we can rewrite \(\frac{(3 + 3 √11) }{ 3}\) as \(\frac{3 (1+√11) }{ 3}\). Since we have a 3 in the numerator and the denominator, we can cancel them out and the answer is 1 + √11.
Forgive me if this is a juvenile question, but can someone explain the leap made from the canceling of the "3's" to the singular "1" preceding the root 11 in the answer:
The expression \(\frac{ 3+3 root 11}{ 3 }\)
The solution is: 1+ root 11
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What your fraction really means is, "\(3 + 3\sqrt{11}\) divided by 3."
In general, to divide a sum (that you can't simplify further) by a number, you divide each part of the sum by that number individually.
For example, 120x + 50y divided by 2, will be 60x + 25y.
We're looking at \(3 + 3\sqrt{11}\), divided by 3. Divide each part by 3: 3 divided by 3 is 1, and \(3\sqrt{11}\) divided by 3 is \(\sqrt{11}\). The sum is 1 + \(\sqrt{11}\).
If you ever want to double check something like this, try plugging it into a calculator when you review. You don't get to use a calculator during the GMAT, but it's fine to use one when you review a problem you've already done, or when you're learning a new concept! In this case, \(3 + 3\sqrt{11}\) is a little bit less than 13. Divide that by 3 to get approximately 4.3. You can then confirm that 1 + [m]\sqrt{11} is approximately 4.3 as well.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.