Question

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

Answer 1

(i) By placing bars, we obtain $64=\overline{64}$

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

(ii) By placing bars, we obtain $144=\overline{1}\overline{44}$

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

(iii) By placing bars, we obtain $4489=\overline{44}\overline{89}$

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

(iv) By placing bars, we obtain $27225=\overline{2}\overline{72}\overline{25}$

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

(v) By placing the bars, we obtain $390625=\overline{39}\overline{06}\overline{25}$

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