show that 2 + root 3 is an irrational number
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Answer:
Step-by-step explanation:
The sum of a rational and an irrational number is an irrational number. (Showed)
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Answer:
Step-by-step explanation:
Let us consider, 2+√3 is rational.
According to the statement above, 2+√3=a÷b, where b≠0
2+√3=a÷b
√3=a÷b-2
√3=a-2b÷b
a-2b÷b is rational,so,√3 is also rational
Therefore, it contradicts the fact that √3 is irrational.
So, we conclude that 2+√3 is irrational number.
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