Find the value of 256 .

Given, 256 We have to find the square root of 256 by prime factorisation method. 2 256 2 128 2 64 2 32 2 16 2 8 2 4 2 2 1 So, 256 = 2 × 2 ⏟ × 2 × 2 ⏟ × 2 × 2 ⏟ × 2 × 2 ⏟ = 4 × 4 × 4 × 4 = 16 × 16 = 16 2 = 16 Hence, the required answer is 16 .

Find the value of 42 . 25 .

We have to find the value of 42 . 25 . We can write this as 42 . 25 = 4225 100 = 4225 100 Now, it is easy to compute the square root of the whole number 4225 by long division method as 4225 = 65 and so, we now get 42 . 25 = 4225 100 = 4225 100 = 65 10 = 6 . 5 Hence, the required answer is 6 . 5 .

Given, 12 × 3 We need to simplify the given terms. Remembering the rule, a × b = a b Here, a = 12 , b = 3 12 × 3 = 12 × 3 = 36 = 6 2 = 6 Hence, the required answer is 6 .

Given, 98 162 We need to simplify the given terms. Remembering the rule, a b = a b b ≠ 0 Here, a = 98 , b = 162 98 162 = 2 × 49 2 × 81 = 49 81 = 7 2 9 2 = 7 9 Hence, the required answer is 7 9 .