Addition Operation with Rational and Irrational Numbers | Irrational numbers proof.
Sum of an irrational number and an irrational number is irrational.
In this video, Irrationality theorem is explained and proof of sqrt(2) is irrational number is illustrated in detail.More emphasis is laid on rational numbers, co-primes, assumption and contradiction of assume statement.One can understand Sum of an irrational number and an irrational number is irrational.
Irrational Numbers Defination:
A number ‘s ’ is called irrational if it cannot be written in the form,p/q where p and q are integers and q is not 0.
Fundamental Theorem of Arithmetic.
Let p be a prime number. If p divides a^2, then p divides a, where a is a positive integer.
00:02 Q2. Prove that 3+2sqrt(5) is irrational.
00:10 Assume contrary of given statement.Take 3+2sqrt(5) is rational.It can be expressed in the for of p/q.Where p and q are prime numbers.
01:35 We get sqrt(5) is rational number which is false.
01:55 Thus our assumption is false.
02:00 3+2sqrt(5) is irrational..
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