Which option correctly tells the role of (5) being prime in the proof of (\sqrt{5})?
Answer and explanation
Correct answer: It lets us conclude that if (p^2) is divisible by (5), then (p) is divisible by (5)
Step 1: If a prime factor divides a square, it also divides the original number. Step 2: Since (5) is prime, (p^2) divisible by (5) implies (p) divisible by (5). Step 3: This is the main logic of the proof.
Frequently asked questions
What is the correct answer to this question?
It lets us conclude that if (p^2) is divisible by (5), then (p) is divisible by (5)
Why is this the correct answer?
Step 1: If a prime factor divides a square, it also divides the original number. Step 2: Since (5) is prime, (p^2) divisible by (5) implies (p) divisible by (5). Step 3: This is the main logic of the proof.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Proof of irrationality of √2, √3, √5.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
