Question

prove that under root 7 is irrational number class 10

Answer 1

Let √7 is a rational number equal to a/b ( where a and b are co-primes ).

⇒ √7 = a/b

Squaring both sides,

⇒ ( √7 )² = ( a/b )²

⇒ 7 = a²/b²

⇒ 7b² = a²

Since 7 is a factor of a², so it will be also factor of a.

Now , assume ( a = 7m ).

⇒ 7b² = ( 7m )²

⇒ 7b² = 49m²

⇒ b² = 49m² / 7

⇒ b² = 7m²

Since 7 is a factor of b², so it will be also factor of b.

So, our assumption that a and b are co-primes is wrong because they have 7 as a factor.It means our assumption that √7 is a rational number is wrong.

Hence, √7 is not a rational number that is it is a irrational number.

Answer 2

Answer:

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