Question

Show that 3 + 2 under root 5 is an irrational number where under root 5 is given to be an irrational number

Answer 1

Answer:

prove:3 + 2√5 is an irrational number.

prove:3 + 2√5 is an irrational number.Proof:

prove:3 + 2√5 is an irrational number.Proof:Letus assume that 3 + 2√5 is a rational number.

prove:3 + 2√5 is an irrational number.Proof:Letus assume that 3 + 2√5 is a rational number.Soit can be written in the form a/b

prove:3 + 2√5 is an irrational number.Proof:Letus assume that 3 + 2√5 is a rational number.Soit can be written in the form a/b3 + 2√5 = a/b

prove:3 + 2√5 is an irrational number.Proof:Letus assume that 3 + 2√5 is a rational number.Soit can be written in the form a/b3 + 2√5 = a/bHere a and b are coprime numbers and b ≠ 0

prove:3 + 2√5 is an irrational number.Proof:Letus assume that 3 + 2√5 is a rational number.Soit can be written in the form a/b3 + 2√5 = a/bHere a and b are coprime numbers and b ≠ 0Solving3 + 2√5 = a/b we get,

prove:3 + 2√5 is an irrational number.Proof:Letus assume that 3 + 2√5 is a rational number.Soit can be written in the form a/b3 + 2√5 = a/bHere a and b are coprime numbers and b ≠ 0Solving3 + 2√5 = a/b we get,=>2√5 = a/b – 3

prove:3 + 2√5 is an irrational number.Proof:Letus assume that 3 + 2√5 is a rational number.Soit can be written in the form a/b3 + 2√5 = a/bHere a and b are coprime numbers and b ≠ 0Solving3 + 2√5 = a/b we get,=>2√5 = a/b – 3=>2√5 = (a-3b)/b

prove:3 + 2√5 is an irrational number.Proof:Letus assume that 3 + 2√5 is a rational number.Soit can be written in the form a/b3 + 2√5 = a/bHere a and b are coprime numbers and b ≠ 0Solving3 + 2√5 = a/b we get,=>2√5 = a/b – 3=>2√5 = (a-3b)/b=>√5 = (a-3b)/2b

prove:3 + 2√5 is an irrational number.Proof:Letus assume that 3 + 2√5 is a rational number.Soit can be written in the form a/b3 + 2√5 = a/bHere a and b are coprime numbers and b ≠ 0Solving3 + 2√5 = a/b we get,=>2√5 = a/b – 3=>2√5 = (a-3b)/b=>√5 = (a-3b)/2bThis shows (a-3b)/2b is a rational number. But we know that But √5 is an irrational number.

prove:3 + 2√5 is an irrational number.Proof:Letus assume that 3 + 2√5 is a rational number.Soit can be written in the form a/b3 + 2√5 = a/bHere a and b are coprime numbers and b ≠ 0Solving3 + 2√5 = a/b we get,=>2√5 = a/b – 3=>2√5 = (a-3b)/b=>√5 = (a-3b)/2bThis shows (a-3b)/2b is a rational number. But we know that But √5 is an irrational number.so it contradictsour assumption.

prove:3 + 2√5 is an irrational number.Proof:Letus assume that 3 + 2√5 is a rational number.Soit can be written in the form a/b3 + 2√5 = a/bHere a and b are coprime numbers and b ≠ 0Solving3 + 2√5 = a/b we get,=>2√5 = a/b – 3=>2√5 = (a-3b)/b=>√5 = (a-3b)/2bThis shows (a-3b)/2b is a rational number. But we know that But √5 is an irrational number.so it contradictsour assumption.Our assumption of3 + 2√5 is a rational number is incorrect.

prove:3 + 2√5 is an irrational number.Proof:Letus assume that 3 + 2√5 is a rational number.Soit can be written in the form a/b3 + 2√5 = a/bHere a and b are coprime numbers and b ≠ 0Solving3 + 2√5 = a/b we get,=>2√5 = a/b – 3=>2√5 = (a-3b)/b=>√5 = (a-3b)/2bThis shows (a-3b)/2b is a rational number. But we know that But √5 is an irrational number.so it contradictsour assumption.Our assumption of3 + 2√5 is a rational number is incorrect.3 + 2√5 is an irrational number

prove:3 + 2√5 is an irrational number.Proof:Letus assume that 3 + 2√5 is a rational number.Soit can be written in the form a/b3 + 2√5 = a/bHere a and b are coprime numbers and b ≠ 0Solving3 + 2√5 = a/b we get,=>2√5 = a/b – 3=>2√5 = (a-3b)/b=>√5 = (a-3b)/2bThis shows (a-3b)/2b is a rational number. But we know that But √5 is an irrational number.so it contradictsour assumption.Our assumption of3 + 2√5 is a rational number is incorrect.3 + 2√5 is an irrational numberHence proved