Question

prove that √5 is an irrational number​

Answer 1

Answer:

it's example is given in class 10th ncert book

chapter 1

veryeasy

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Answer 2

Nice I can prove

Just write as I write this question includes lots of statements

A rational no. is. no. which is in the form of p/q where p and q have no common factor and q is not equal to 0

Let √5 be assumed as a rational no.

so

√5= p/q

Squaring both sides

(√5)² = p²/q²

5= p²/q²

Cross Multiplying both sides

p²= 5q²

As 5 divides 5q²

it will also divide p²

so 5 will divide p

Let p=5k(where k is an integer)

squaring both sides

p²= 25k²

5q²= 25k²

q²=25k²/5

q² = 5k²

Since 5 divides 5k²

it will also divide q²

since it divides q² it will divide q too

Thus p and q have common factor 5 .This contradicts our assumption that p and q have no common factor ( except 1)

Therefore√5 is an irrational no.