Question

सिद्ध कीजिए कि रूट 7 एक अपरिमेय संख्या है​

Answer 1

Answer:

समीकरण (i ) तथा (ii ) से हम कह सकते है कि a और b का कम से कम एक गुणनखंड 3 है । परन्तु यह इस तथ्य का विरोधाभास करता है कि a और b सह-अभाज्य है। इसका अर्थ यह है कि हमारी परिकल्पना सही नहीं है। अतः √3 एक अपरिमेय संख्या है।

this is not right answer

Answer 2

(｡◕‿◕｡)

Answer:

• 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.