NCERT Solutions Class 10 Maths Chapter 1 — Real Numbers

Solution:

Step 1: Find the factors of each number:

Step 2: Factors of 12: [12 = 2 x 2 x 3]

Step 3: Factors of 18: [18 = 2 x 3 x 3]

Step 4: Common factors: 2 and 3 [HCF = 2 x 3 = 6]

Solution:

Step 1: Prime factorisation:

Step 2: 4 = 2 x 2 and 6 = 2 x 3

Step 3: Take the highest power of each prime: [LCM = 2^2 x 3 = 12]

Solution:

Step 1: 3/7 is rational (ratio of two integers)

Step 2: 0.25 = 1/4 is rational

Step 3: 0.333... = 1/3 is rational (repeating decimal)

Step 4: sqrt(5) cannot be written as p/q, so it is irrational

Solution:

Step 1: In Euclid's division algorithm, we divide the larger number by the smaller:

Step 2: 455 / 42 gives quotient 10 and remainder 35 [455 = 42 x 10 + 35]

Step 3: We then apply the algorithm to 42 and 35

Solution:

Step 1: Divide step by step: [56 / 2 = 28]

Step 2: Continue: [28 / 2 = 14]

Step 3: Continue: [14 / 2 = 7]

Step 4: 7 is prime, so: [56 = 2^3 x 7]