Math CentralQuandaries & Queries


Question from Serena, a student:

Inequalities for numbers between 0 and 1:

If 0 is less than x and x is less than 1 then is the square root of x greater than x?

How is the square root of 3/4 is greater than 3/4?

Hi Serena,

3 × 3 = 9 so the square root of 9 is 3.

1/2 × 1/2 = 1/4 so the square root of 1/4 is 1/2.

The reason that the square root of 3/4 is larger than 3/4 is exactly what you said, 3/4 is between 0 and 1. If you take a positive number y and multiply it by a number x where x is between 0 and 1 then the product is smaller than y since you are taking a fractional part of y.

I hope this helps,

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