please answer any one question from this
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please answer any one question from this
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Answer:
Let √3 + √5 be a rational number , say r
then √3 + √5 = r
On squaring both sides,
(√3 + √5)2 = r2
3 + 2 √15 + 5 = r2
8 + 2 √15 = r2
2 √15 = r2 - 8
√15 = (r2 - 8) / 2
Now (r2 - 8) / 2 is a rational number and √15 is an irrational number .
Since a rational number cannot be equal to an irrational number
Answer:
To show √3+√5 us an irrational number.
First, assume √3+√5 as rational
if √3+√5 is a rational
√3+√5 =a/b(where a and b are co primes)
now,
√3+√5=a/b
√5=a/b-√3
therefore, a/b-√3 is a rational number
and √5 is an irrational number
hence, we know an irrational number is not equal to rational number.
hence, the assumption was wrong.
The contradiction has arising due to wrong assumption.
therefore, √3+√5 is an irrational number.
hence proved.