Roots Problem

[ajainkur]

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?

[Whitney Garner]

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

[HerrGrau]

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.

[Jim@StratusPrep]

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.