Sum and Product of rational and irrational numbers is Irrational | Proving Irrational numbers
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.
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.
00:02 Q3. Prove that the following are irrationals :
(i)1/sqrt(2) (ii)7sqrt(5) (iii) 6+sqrt(2)
00:20 prove 1/sqrt(2) is irrational number
00:25 Assume contrary of given statement.Take 1/sqrt(2) is rational.It can be expressed in the for of p/q.Where p and q are prime numbers.
01:08 we get sqrt(2) is rational which is false.
This is because of our wrong assumption.
01:32 Thus 1/sqrt(2) is irrational number is proved
CBSE solutions for class 10 maths Chapter 1 Real Numbers Exercise 1.4
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