Question

1. Prove that 15 is irrational.
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Answer 1

Step-by-step explanation:

let √15 be a rational no if the form of p/q where p and q are ration no.

=>√15=p/q

squaring both sides

=>15= p²/q²

q²=p²/15---(1)

15 divides p and p is a multiple of 15

=>p = 15m

=>p²= 225m²---(2)

From equations (1) and (2), we get,

=>15q² = 225m²

=>q² = 15m²

=>q² is a multiple of 15

=>q is a multiple of 15

Hence, p, q have a common factor 15. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number

√5 is an irrational number.