Q) Find by prime factorisation the LCM of the numbers 18180 and 7575. Also, find the HCF of the two numbers. Ans: By prime factorisation, we get: 18180 = 22 x 32 x 5 x 101 and 7575 = 3 x 52 x 101 LCM = 22 x 32 x 52 x 101 LCM = […]
real numbers
Q) Prove that 2 + √3 is an irrational number, given that √3 is an irrational number. Ans: Let us assume that 2 + √3 is a rational number Let 2 + √3 = ; q ≠ 0 and p, q are integers √3 = Since, p and q are integers; Therefore p – 2q is
Prove that 2 + √3 is an irrational number, given that √3 is an irrational number. Read More »
Q) Find the least number which when divided by 12, 16 and 24 leaves remainder 7 in each case. Ans: Let’s start with LCM of 12, 16, 24: We get LCM as 48 Since remainder is 7, It means the number is 7 more than LCM Hence, the required number is 48 + 7 =
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