Question

can anyone solve this .plz tomorrow is my exam.

Answer 1

some questions
are not clear and only allowed
to attach 1 pic so

Answer 2

7Q.prove that √2 is an irrational number and (5+3√2) Is an irrational number
solu- let √2 is a rational number
p/q = √2 (where p and q are co-prime)
p =√2q
(p) 2= (√2q)2
p2 = 2q2
therefore, 2 is factor of p
again,
p= 2r
(2r) 2 =(2q) 2
4r = 2q2
2r = q2
therefore, 2 is à Factor of q
As 2 is à common factor of p ana
thus , we came à wrong conclusion as Our consideration at thé beginning was wrong
therefore, √2 is an irrational number



second part,
prove that ( 5 +3√2) is an irrational number
5+3√2= p/q
3√2 =p/q-5
√2=p-5q/2q
therefore, p-5q/2q is rational number so, √2 is also rational number but we know that √2 is irrational number.
so,
we came to a wrong conclusion as Our consideration at thé beginning was wrong.
( 5 +3√2) is an irrational number