Question

prove that 3+ underroot 5 ​

Answer 1

Answer:

as p, q and 3 are integers p-3q/3 is a rational number. ... this contradiction has arisen because of our wrong assumption that 3+root 5 is a rational number. hence 3+ root 5 is an irrational number.

Answer 2

Step-by-step explanation:

• let us assume that 3+ root5 is a rational no
• there fore,3+root5=p/q where p,a are integers,q is not equal to 0
• 3+root5=p/a
• squaring on both sides, we get
• (3+root5)^2=(p/q)^2

9+5+6root5=p^2/q^2

14+6root5 =p2/q2

6 root5=p^2-14q^2/q^2

root5=p^2-14q^2/6q^2

• we know that p,q,14,6 are rational nos. as they are integers.
• but root5 is an irrational no.
• Irrational no. is not equal to rational no.
• hence our prediction that 3+ root5 is rational no is wrong.
• therefore 3+root5 is an irrational no.