Correct Answer - Option 1 : 7

**Formula Used:**

Remainder Theorem

Dividend = (Divisor × Quotient) + Remainder

**Calculation:**

(19 × 109 × 1009 × 10009)/100

We will calculate the remainder in each term and then multiply the remainders

(19 × 9 × 9 × 9)/100 = (19 × 729)/100

Continue this process until we get a remainder less than 100

⇒ (19 × 29)/100

⇒ 551/100

⇒ 51/100

**R = 51**

√(R – 2)

⇒ √(51 – 2)

⇒ √49 = 7

**∴ ****Required value is 7.**