Mathematics : Real Numbers

• terminating decimal 
• non-terminating decimal
• non-terminating repeating decimal 
• non-terminating repeating decimal 

• composite number

• composite number

• any natural number
• any natural number

• 51
• 15
• 50
• 50

• 5
• 7 
• 3 
• 3 

• 2

• 8

• 0

• 0

• 31

• 32

• 33

• 33

• 9q + 1 
• 9q 4 + 8 
• both (a) and (b)
• both (a) and (b)

•  a = bq + r, 0 ≤ r < b; a, b, q, r ∊ Integers
• a = bq - r, 0 ≤ r < b
• a = bq - r, 0 ≤ r < b
• a = bq - r, 0 ≤ r < b

What is the HCF of the smallest prime number and the smallest composite number?

Given that  is irrational, prove that  is an irrational number.