real numbers

Q)  Prove that √5 is an irrational number.  Ans:  Let √5 be a rational number. Therefore √5 = p/q, where q ≠ 0 and let p & q be co-primes. ⇒ 5q² = p² ⇒ p² is divisible by 5 ⇒ p is divisible by 5………………….. ……………….. (i) ⇒ p = 5a, where a is some […]

Q)  Find the greatest number which divides 85 and 72 leaving remainders 1 and 2 respectively. Ans:  Question is asking for highest number which is dividing other numbers…. . clearly, we need to find HCF Since there are remainders after dividing, hence if we subtract remainder from the given number, we will get the actual