Question

The different between
`√(7)` and
`√(2)` is a/an rational __________.

Answer 1

irrational

Step-by-step explanation:

What a rational is:

a number that can be given as the ratio of two integers

We know that √2 cannot be given as a ratio of two integers.

(√7 also cannot be given as a ratio of two integers)

[What an irrational number is:

a number that cannot be given as the ratio of two integers]

This makes √2 and √7 irrational numbers.

When subtracting √2 from anything, (other than √2) you end up with an irrational number. [or √7]

0 - √2 = irrational

10204 - √2 = irrational

4 - √2 = irrational

So, when subtracting √2 from √7, (finding the difference between the two), we are left with an irrational number.