Question

Prove that 3+√5 is an irrational number urgent dont spam​

Answer 1

Answer:

Let us assume that is a rational number. ⇒ 3 + 5 = p q , where p and q are the integers and q ≠0. ... This contradiction has arisen due to the wrong assumption that is a rational number. Hence, is an irrational number.

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Answer 2

Step-by-step explanation:

10th

Maths

Real Numbers

Revisiting Irrational Numbers

prove that 3 + √(5) is an ...

MATHS

prove that 3+

5

is an irrational number.

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ANSWER

Let us assume that 3+

5

is a rational number.

Now,

3+

5

=

b

a

[Here a and b are co-prime numbers]

5

=[(

b

a

)−3]

5

=[(

b

a−3b

)]

Here, [(

b

a−3b

)] is a rational number.

But we know that

5

is an irrational number.

So, [(

b

a−3b

)] is also a irrational number.

So, our assumption is wrong.

3+

5

is an irrational number.

Hence, proved.