Question

proove that root 5is irrational

Answer 1

Hey!

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Let assume that √5 is a rational number

So we can find coprime integers a and b

b ≠ 0

√5 = a ÷ b

√5b = a

Squarring both sides

(√5b)² = a²

5b² = a²

5 divides a² and 5 also divides a (Therom)

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Now :-

a = 5c for some integer c

5b² = (5c)²

5b² = 25c²

b² = 5c²

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5 divides b² than 5 also divides b (Therom)

A and b have a common factor 5 other than 1 which is contrary to the fact that a and b are Co Prime.

Our supposition is not correct

Hence √5 is an irrational number

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Regards :)

Cybary

Be Brainly :)

Answer 2

Heya !!!


If possible , suppose ✓5 is rational Number.

✓5 = A/B , where a and b are Integers and B not equal 0.

Let A and B have some common factor other than 1, then Divides A and B by that common factor .


Squaring both sides,


✓5 = A/B

(✓5)² = (A/B)²


5 = A²/B²


A² = 5B² -------(1)


5 Divides A² => 5 Divides A.

Let A = 2K , where K is some integer.


Putting A = 2K in equation (1)


25K² = 5B² => B² = 5K²

=> 5 Divides B² => 5 Divides B.


We see that A and B have common factor other than 5. Which is contradiction to the fact that a and b are Co prime.


Therefore,

Our SUPPOSITION is wrong that ✓5 is rational Number.


Hence,


✓5 is irrational Number.

HOPE IT WILL HELP YOU..... :-)