Math, asked by HisiteshRJain, 10 months ago

prove that √5 is irrational ​

Answers

Answered by shrishtisharma2501
3

Answe

It's a irrational as it can't be written in p/q form.

√5 is an irrational number

Hence proved

Step-by-step explanation:

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Answered by Anonymous
4

Answer:

here is your answer dude...

Step-by-step explanation:

ANSWER

Let

5

be a rational number.

then it must be in form of

q

p

where, q

=0 ( p and q are co-prime)

5

=

q

p

5

×q=p

Suaring on both sides,

5q

2

=p

2

--------------(1)

p

2

is divisible by 5.

So, p is divisible by 5.

p=5c

Suaring on both sides,

p

2

=25c

2

--------------(2)

Put p

2

in eqn.(1)

5q

2

=25(c)

2

q

2

=5c

2

So, q is divisible by 5.

.

Thus p and q have a common factor of 5.

So, there is a contradiction as per our assumption.

We have assumed p and q are co-prime but here they a common factor of 5.

The above statement contradicts our assumption.

Therefore,

5

is an irrational number.

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