Dentify square root of 2 as either rational or irrational, and approximate to the tenths place. a. rational: square root of 2 ≈ 1.5 irrational: b. square root of 2 ≈ 1.5 rational: c. square root of 2 ≈ 1.4 irrational: d. square root of 2 ≈ 1.4

The square root of two is irrational. It means that you can't write it as a fraction:

Here's a proof. Assume that you could write

for some integers p and q, and that p and q have no common divisors. If you square both sides you have

So, is even, which means that also p is even, and thus there exists some number k such that . The expression becomes

So, also is even, and thus q is also even.

But then, p and q are both even, whereas we assumed that they had no common divisors. Contraddiction.

As for the value, any calculator will give you an approximation that starts with

so, it is best approximated by 1.4.

step-by-step explanation: