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Prove that 3+2√5 is irrational number

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Prove that 3+2√5 is irrational number

Posted by Chandan Mishra 5 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

Yogita Ingle 5 years, 10 months ago

Let take that 3 + 2√5 is a rational number.
So we can write this number as
3 + 2√5 = a/b
Here a and b are two co prime number and b is not equal to 0
Subtract 3 both sides we get
2√5 = a/b – 3
2√5 = (a-3b)/b
Now divide by 2 we get
√5 = (a-3b)/2b
Here a and b are integer so (a-3b)/2b is a rational number so √5 should be a rational number But √5 is a irrational number so it contradict the fact
Hence result is 3 + 2√5 is a irrational number

0Thank You

Alka Sharma 5 years, 10 months ago

Let 3+2√5 be a rational no. 3+√5=a/b (a & b are co-prime no.) √5=a-3b/b (we know that √5 is a irrational no) This contradict the fact that 3+√5 is a irrational no.

1Thank You

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