Question

prove that 3+2√5 is irrational.
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Answer 1

Answer:Given: 3 + 2√5

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

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

Given: 3 + 2√5To prove: 3 + 2√5 is an irrational number.Proof:Let us assume that 3 + 2√5 is a rational number.

Given: 3 + 2√5To prove: 3 + 2√5 is an irrational number.Proof:Let us assume that 3 + 2√5 is a rational number.So, it can be written in the form a/b

Given: 3 + 2√5To prove: 3 + 2√5 is an irrational number.Proof:Let us assume that 3 + 2√5 is a rational number.So, it can be written in the form a/b3 + 2√5 = a/b

Given: 3 + 2√5To prove: 3 + 2√5 is an irrational number.Proof:Let us assume that 3 + 2√5 is a rational number.So, it can be written in the form a/b3 + 2√5 = a/bHere a and b are coprime numbers and b ≠ 0

Given: 3 + 2√5To prove: 3 + 2√5 is an irrational number.Proof:Let us assume that 3 + 2√5 is a rational number.So, it can be written in the form a/b3 + 2√5 = a/bHere a and b are coprime numbers and b ≠ 0Solving 3 + 2√5 = a/b we get,

Given: 3 + 2√5To prove: 3 + 2√5 is an irrational number.Proof:Let us assume that 3 + 2√5 is a rational number.So, it can be written in the form a/b3 + 2√5 = a/bHere a and b are coprime numbers and b ≠ 0Solving 3 + 2√5 = a/b we get,=>2√5 = a/b – 3

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

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

Given: 3 + 2√5To prove: 3 + 2√5 is an irrational number.Proof:Let us assume that 3 + 2√5 is a rational number.So, it can be written in the form a/b3 + 2√5 = a/bHere a and b are coprime numbers and b ≠ 0Solving 3 + 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 √5 is an irrational number.

Given: 3 + 2√5To prove: 3 + 2√5 is an irrational number.Proof:Let us assume that 3 + 2√5 is a rational number.So, it can be written in the form a/b3 + 2√5 = a/bHere a and b are coprime numbers and b ≠ 0Solving 3 + 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 √5 is an irrational number.So, it contradicts our assumption. Our assumption of 3 + 2√5 is a rational number is incorrect.

Given: 3 + 2√5To prove: 3 + 2√5 is an irrational number.Proof:Let us assume that 3 + 2√5 is a rational number.So, it can be written in the form a/b3 + 2√5 = a/bHere a and b are coprime numbers and b ≠ 0Solving 3 + 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 √5 is an irrational number.So, it contradicts our assumption. Our assumption of 3 + 2√5 is a rational number is incorrect.3 + 2√5 is an irrational number

Given: 3 + 2√5To prove: 3 + 2√5 is an irrational number.Proof:Let us assume that 3 + 2√5 is a rational number.So, it can be written in the form a/b3 + 2√5 = a/bHere a and b are coprime numbers and b ≠ 0Solving 3 + 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 √5 is an irrational number.So, it contradicts our assumption. Our assumption of 3 + 2√5 is a rational number is incorrect.3 + 2√5 is an irrational numberHence proved

Explanation:

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