0 reads0 ratings0 helpful
After assuming (\sqrt{5}) rational and getting (a^2=5b^2), how does a common factor appear in (a) and (b)?
Advertisement
Answer and explanation
Correct answer: First (5\mid a), then substituting (a=5k) gives (5\mid b)
Step 1: From (a^2=5b^2), (5\mid a). Step 2: Putting (a=5k) gives (b^2=5k^2), so (5\mid b). Step 3: Now (5) becomes a common factor and gives the contradiction.
Frequently asked questions
What is the correct answer to this question?
First (5\mid a), then substituting (a=5k) gives (5\mid b)
Why is this the correct answer?
Step 1: From (a^2=5b^2), (5\mid a). Step 2: Putting (a=5k) gives (b^2=5k^2), so (5\mid b). Step 3: Now (5) becomes a common factor and gives the contradiction.
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?
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Difficulty
Easy0%
Medium0%
Hard0%
Was the explanation clear?
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
Advertisement