please solve this all problems with process please
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please solve this all problems with process please
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Let us assume that √2 is a rational number.
So, √2= a / b (a and b are co prime i.e. no common factor other than 1)
=> √2b = a
squaring both sides
(√2b)²= a²
=> 2b² = a²
As 2 divides a² ,it will also divide a.
Now, let a = 2c (where c is some integer)
We know that,
a² = 2b²
putting a = 2c in above equation
(2c)²=2b²
4c²=2b²
2c²=b²
Hence, 2 divides b², it will also divide b.
So, 2 is a factor of a and b both as 2 divides a and b.
But we have assumed that they are co prime and cannot have any common factor other than 1.
This contradicts our assumption.
Hence, our assumption is wrong.
√2 is irrational number.
By using exactly same method you can solve the other parts.
P.S. Please mark as brainliest.