Question

Identify square root of 2 as either rational or irrational, and approximate to the tenths place.

Answer 1

√2 is irrational because let's suppose √2 is a rational number. Then, we write
√2=a/b where a and b are whole number, b≠0
From the equality √2=a/b, it follows that 2= a²/b²( Make all of them to the second power), or a²=2×b²
Then, a is 2 times some other whole number. In symbols, a=2k where k is this other number
If we substitute a=2k into the original equation 2=a²/b², this is what we get:
2=(2k)²/b²
2=4k²/b²
2b²=4k²
b²=2k². This means that b² is even, from which follows again that b itself is we . And that is contradiction, and thus our original assumption (that √2 is rational). Therefore, √2 can not be rational
√2=1.41421356237..
√2=1.4( rounded to the nearest tenth). Hope it help!