Problem Solving

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?

Hi ajainkur!

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