Prove that 3-2√7 is irrational number
Answers
Given: The term 3-2√7.
To find: Prove that 3 - 2√7 is an irrational number.
Solution:
- Now we have given the term: 3 - 2√7
- Consider 3 - 2√7 as a rational number, then we can write it in the form of a/b, where a and b are co prime.
3 - 2√7 = a/b
-2√7 = a/b - 3
-2√7 = (a-3b)/b
√7 = (-a+3b)/2b
- So this proves that (3b - a)/2b is a rational number.
- But √7 is an irrational number so it contradicts our assumption.
- So our assumption is wrong.
3 - 2√7 is an irrational number.
Answer:
So 3 - 2√7 is an irrational number.
Answer:
Now we have given the term: 3 - 2√7
Consider 3 - 2√7 as a rational number, then we can write it in the form of a/b, where a and b are co prime.
3 - 2√7 = a/b
-2√7 = a/b - 3
-2√7 = (a-3b)/b
√7 = (-a+3b)/2b
So this proves that (3b - a)/2b is a rational number.
But √7 is an irrational number so it contradicts our assumption.
So our assumption is wrong.
3 - 2√7 is an irrational number.
Step-by-step explanation: