Question

Prove that root 3 and root 5 is irrational

Answer 1

Heya!!!

↪ Here's your answer friend,

Let √3 be a rational number

==> √3 = a / b...... ( where a and b are coprime numbers and b ≠ 0)

==> Squaring on both sides

we get,

3 = a² / b²

==> a² = 3b² .......(1)

==> 3 | a²

==> 3 | a


==> a = 3c........ ( if b|a then a = bc)

==> On squaring both the sides

we get,

==> a² = (3c)²

==> a² = 9c²

==> 3b² = 9c²

==> b² = 3c²

==> 3 | b²

==> 3 | b


From above we get 3 divides both a and b.
But a and b are coprime numbers

therefore our assumption proved wrong

√3 is an irrational number.

Similarly, √5 is an irrational number.

⭐ Hope it helps you : ) ⭐