Find the square root of the following: 1183 2023

We know, To find the square root of a rational number, If a , b are any two whole numbers, b ≠ 0 , then a b = a b . To find the square root of a number by prime factorisation method, follow the below given steps. Find the prime factors of the given number. Make pairs of the smaller factors. Take one factor from each pair and multiply together. Now, Start finding the square root by prime factorisation as done for natural number. Given, 1183 2023 Therefore, we get: 7 1 1 8 3 13 1 6 9 13 1 3 1 7 2 0 2 3 17 2 8 9 17 17 1 That is, 1183 2023 = 7 × 13 × 13 7 × 17 × 17 ⇒ 1183 2023 = 7 × 13 7 × 17 = 13 17 Hence, 1183 2023 = 13 17 .

Find the value of 0 . 0441 , and using this value, calculate 441 + 0 . 000441 .

We know, Follow the below given steps to find the square root of the rational numbers in decimal form: Obtain the given number in the decimal form. Place a bar or comma on the integral part similar to the way we do in finding square root of natural number. Place a bar or comma on the decimal part on every pair of digits beginning with decimal places. If any single place is left in the last, then affix a zero on the extreme right of the decimal part to make a pair. Start finding the square root by long division process as done for natural number. Place a decimal point in the quotient as soon as the integral part is exhausted. Stop the process when the remainder is zero. The quotient so obtained is the required square root. Given numbers are 0 . 0441 , 441 , 0 . 000441 Therefore, we get the square root as: 0 . 2 1 0 . 0 4 , 4 1 0 2 0 0 4 4 41 0 4 1 4 1 0 Therefore, 441 = 21 0 . 000441 = 0 . 021 Thus, we get: 441 + 0 . 000441 = 21 + 0 . 021 = 21 . 021 Hence, the required value is 21 . 021 .