will the numbers relation for such type of problems still work if we square them all ? then add the -ve sign, so its easier to deal with solid numbers than roots?

amyhussein wrote:Hello

How can i do the problem below in a faster way/shortcut:

Organize the following numbers from lowest to biggest:

-√5/5 , -√7/7 , -5/√5 , -7/√7 , -1

To organize the values in the correct order, we need to determine their RELATIVE distances from 0.
Since all of the values are negative, the GREATER the distance from 0, the SMALLER the value.
To determine the relative distances, square all of the values and retain the negative signs:
-√5/5 --> -(√5/5)² = -1/5

-√7/7 --> -(√7/7)² = -1/7

-5/√5 --> -(5/√5)² = -5

-7/√7 --> -(7/√7)² = -7

-1 --> -(1²) = -1


The least value = the value furthest from 0 = -7/√7.
The greatest value = the value closest to 0 = -√7/7.
From least to greatest:

-7/√7, -5/√5, -1, -√5/5, -√7/7.