show that 5 - 2√3 is an irrational number?
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ANSWER:
5-2√3 is an irrational number.
TO PROVE:
- 5-2√3 is an IRRATIONAL number.
SOLUTION:
Let 5-2√3 is a rational number which can be expressed in the form of p/q where p and q have no common factor other than one.
This shows that √3 is a Rational number But we know that √3 is an Irrational number. Thus our supposition was wrong so 5-2√3 is an Irrational number.
NOTE:
- The root of all prime number is an Irrational number.
- The above method of proving irrational number is called contradiction method.
- In contradiction method we first suppose the Wrong but at last we prove that our supposition is wrong.
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