Question

prove that root 7 is an irrational number and hense show that 3-2root 7 is irrational​

Answer 1

let √7 be a rational number.

then,

√7 = p/q (where p and q are integers and q is not equal to zero)

Squaring Both sides

(√7)² = (p/q)²

7 = p²/q²

7q² = p²

here we see that,

7 divides p

and

7 also divides p².......(¡)

let p be 7

so,

7q² = p²

7q² = (7)²

7q² =49

7 = q²

here we see that,

7 divide q

7 also divides q².....(¡¡)

so, from (¡) and (¡¡)

we get

Our assumption wrong.

√7 is an irrational number.

Answer 2

Answer:

Step-by-step explanation:

let 3-2root7 is rational

3-2root7=p/q

root7=p-3q/2q

since p and q are integers

so p-3q/2q is rational but root 7 is ir rational therefore our assumption is wrong