Question

prove √5 is an irrational number​

Answer 1

Answer:

to the contrary let us assume that √5 is ratuonal so it can be expressed in from of p/q where p and q are co prime integer

√5 = p/q

squaring both side..

√5² = (p/q)²

5 = p² / q²

5q² = p². ....(1)

p² is divisible by 5

p is divisible by 5 ...(2)

put p = 5c in eq..(1)

5q² = (5c)²

q²= 25c²/5

q²= 5c²

q² is divisible by 5

q is divisible by 5 .... (3)

from eq.1 and eq..2 we get that p and q have common factor 5 but this contradicts the fact that p and q are co prime ....

so this contradiction arisen due to our wrong assumption that√5 is rational

therefore √5 is irrational

hence proved. ....

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Answer 2

Answer:

hey mate sry .......

here is Ur answer ,.....

bye