prove thai √7 is an irrational number
Answers
Answer:
Hope the answer helps you
Step-by-step explanation:
Given √7
To prove: √7 is an irrational number.
Proof:
Let us assume that √7 is a rational number.
So it t can be expressed in the form p/q where p,q are co-prime integers and q≠0
√7 = p/q
Here p and q are coprime numbers and q ≠ 0
Solving
√7 = p/q
On squaring both the side we get,
=> 7 = (p/q)2
=> 7q2 = p2……………………………..(1)
p2/7 = q2
So 7 divides p and p and p and q are multiple of 7.
⇒ p = 7m
⇒ p² = 49m² ………………………………..(2)
From equations (1) and (2), we get,
7q² = 49m²
⇒ q² = 7m²
⇒ q² is a multiple of 7
⇒ q is a multiple of 7
Hence, p,q have a common factor 7. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number
√7 is an irrational number.
Answer:
Just make it rational and predict it as irrational
Btw dude can I get yur intro ?