Math, asked by rohithkunchakuri, 11 months ago



2. Prove that 3+2 V5 is an irrational number.

Answers

Answered by arpita8316
0

Let us assume that 3 + 2 root 5 is irrational number.

Now,let 3+2root 5=a/b b is not equal to 0

2root5 =a/b_3

root5=a/2b_3/2

since A and B are integers therefore a / 2 b_ 3 /2 is a rational number.

root5 is an irrational no.

So,3+2root5 is an irrational no. .

Answered by Anonymous
3

Answer:

Yes, 3 + 2√5 is a irrational number.

Step-by-step explanation:

Let assume 3 + 2√5 is a rational number.

So,

\tt{\implies 3+2\sqrt{5} =\dfrac{p}{q}}

[Where p and q are integers, q ≠ 0 & p and q are co-prime numbers.]

\tt{\implies 2\sqrt{5}=\dfrac{p}{q}-3}

\tt{\implies 2\sqrt{5}=\dfrac{p-3q}{q}}

\tt{\implies \sqrt{5}=\dfrac{p-3q}{2q}}

We know that \tt{\dfrac{p-3q}{2q}} is rational number. But we also know √5 is irrational number.

And we also know Irrational ≠ rational

Hence, our assumption is wrong

3 + 2√5 is a irrational number.

#answerwithquality

#BAL

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