Sal proves that the square root of 2 is an irrational number, i.e. it cannot be given as the ratio of two integers.
Why is √ 2 an irrational number?
Specifically, the Greeks discovered that the diagonal of a square whose sides are 1 unit long has a diagonal whose length cannot be rational. By the Pythagorean Theorem, the length of the diagonal equals the square root of 2. So the square root of 2 is irrational!
How do you prove √ 2 is irrational?
Proof that root 2 is an irrational number.
- Answer: Given √2.
- To prove: √2 is an irrational number. Proof: Let us assume that √2 is a rational number. So it can be expressed in the form p/q where p, q are co-prime integers and q≠0. √2 = p/q. ...
- Solving. √2 = p/q. On squaring both the sides we get, =>2 = (p/q)2
