Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number”,

Solution:  Let us assume, to the contrary, that √3 is rational.  So, we can find coprime integers a and b(b ≠ 0)  such that √3 = a/b  => √3b = a  => 3b2 = a2 ….(i) [Squaring both the sides]  => a2 is divisible by 3  =>...

Solution: Let us assume, to the contrary that 4 - 5√2 is rational. So, we can find coprime integers a and b(b ≠ 0) such that 4 - 5√2 = a/b => 5√2 = 4 -...

Solution:  Let us assume, to the contrary that 5 + 3√2 is rational.  So, we can find coprime integers a and b(b ≠ 0)  such that 5 + 3√2 = a/b  => 3√2 = a/b - 5 => √2 = (a - 5b)/3b  Since...

Solution: The product of a rational number and an irrational number can be a rational number or an irrational number. Examples: i. rational number = 0 irrational number = √2 => 0 x √2 = 0, which...

The product of a non zero rational and an irrational number is always irrational 

It is (B) an irrational number 

The reciprocal of an irrational number is an irrational

Correct answer is (D) always a non-zero number

Let √3 − √2 = r where r be a rational number  Squaring both sides  ⇒ (√3-√2)2= r2  ⇒ 3 + 2 - 2 √6 = r2  ⇒ 5 - 2 √6 = r2   Here, 5 - 2√6 is...

√(2 × 3) = √6