Find the number of digits in the square root of each of the following numbers (without any calculation)

(i) 64 (ii) 144

(iii) 4489 (iv) 27225

(v) 390625

(i) By placing bars, we get

64 = 6̅4̅

Since there is only one bar, the square root of 64 will have only one digit in it

(ii) By placing bars, we get

144 = 1̅ 4̅4̅

Since there are two bars, the square root of 144 will have 2 digits in it

(iii) By placing bars, we get

4489 = 4̅4̅ 8̅9̅

Since there are two bars, the square root of 4489 will have 2 digits in it

(iv) By placing bars, we get

27225 = 2̅ 7̅2̅ 2̅5̅

Since there are three bars, the square root of 27225 will have three digits in it

(v) By placing the bars, we get

390625 = 3̅9̅ 0̅6̅ 2̅5̅

Since there are three bars, the square root of 390625 will have 3 digits in it