While practicing, i stumbled on below question and found it very time consuming to solve it
question was if M = square root of 4 + cube root of 4 + 4th root of 4, then what is the value of M
a. Less than 3
b. equal to 3
c. in between 3 and 4
d. greater than 4
e. equal to 4
could someone suggest how to approach these sort of questions?
Roots Problem
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Hi ajainkur!ajainkur wrote:While practicing, i stumbled on below question and found it very time consuming to solve it
question was if M = square root of 4 + cube root of 4 + 4th root of 4, then what is the value of M
a. Less than 3
b. equal to 3
c. in between 3 and 4
d. greater than 4
e. equal to 4
could someone suggest how to approach these sort of questions?
Always keep an eye on the answer choices - we don't need a good estimate, just a rough guess. So let's see what we know. We know that the square root of 4 is just 2, so that is a start. Now let's use benchmarking for the roots we don't know.
For the cubed root, let's think about perfect cubes we do know...well cuberoot(1)=1, and the cuberoot(8)=2, so the cuberoot(4) must be between 1 and 2.
For the fourth root, let's think about perfect fourths we do know...well 4th_root(1)=1, and the 4th_root(16)=2, so the 4th_root(4) must be between 1 and 2.
Now we put this all together:
sqrt(4) + 3root(4) + 4root(4)
2 + (1.something) + (1.something)
= A number LARGER than 4!
Whit
Whitney Garner
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Math is a lot like love - a simple idea that can easily get complicated
GMAT Instructor & Instructor Developer
Manhattan Prep
Contributor to Beat The GMAT!
Math is a lot like love - a simple idea that can easily get complicated
- HerrGrau
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Hi,
A great way to do these types of questions is to set up a a few inequalities and then add them together. For roots that you do not know take the perfect root below the number and the perfect root above the number to create the range.
2 + 1<x<2 + 1<x<2 = m
Then add them together and 4<m<6. This method works on a variety of questions. Be comfortable setting up inequalities. And be comfortable adding inequalities to create a range of values.
I hope this helps!
HG.
A great way to do these types of questions is to set up a a few inequalities and then add them together. For roots that you do not know take the perfect root below the number and the perfect root above the number to create the range.
2 + 1<x<2 + 1<x<2 = m
Then add them together and 4<m<6. This method works on a variety of questions. Be comfortable setting up inequalities. And be comfortable adding inequalities to create a range of values.
I hope this helps!
HG.
"It is a curious property of research activity that after the problem has been solved the solution seems obvious. This is true not only for those who have not previously been acquainted with the problem, but also for those who have worked over it for years." -Dr. Edwin Land
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This is all about estimation as was said. Just a quick tid bit:
If you are take any number greater than 1, no matter what root you take it will always be greater than 1. So, the 100th root of 1.2 is still larger than 1. This thought helps simplify the work.
If you are take any number greater than 1, no matter what root you take it will always be greater than 1. So, the 100th root of 1.2 is still larger than 1. This thought helps simplify the work.
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-- Push button course navigation to simplify planning
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