Question

10. (a) Show that√7 is irrational.​

Answer 1

Answer:

let us assume that √7 be rational. thus q and p have a common factor 7. as our assumsion p & q are co prime but it has a common factor. So that √7 is an irrational.

Step-by-step explanation:

then it must in the form of p / q  [q ≠ 0] [p and q are co-prime]

√7 = p / q

=> √7 x q = p

squaring on both sides

=> 7q²= p²  ------  (1)

p² is divisible by 7

p is divisible by 7

p = 7c  [c is a positive integer] [squaring on both sides ]

p² = 49 c² ---------   (2)

Subsitute p² in equ (1)

we get

7q² = 49 c²

q² = 7c²

=> q is divisible by 7 thus q and p have a common factor 7. there is a contradiction as our assumsion p & q are co prime but it has a common factor. So that √7 is an irrational.

Answer 2

Answer:

see the attached image above...

Step-by-step explanation:

it has explained step by step...

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