2.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

We know that if n is number of digits in a perfect square number, then it's square root will have \(\frac{n}2\) digits if n is even and \{\frac{(n+1)}2\) digits if n is odd.
(i) 64

Here n is even i.e, 2.

So, number of digits in \(\sqrt{64} = \frac { 2 }{ 2 } = 1\)

(ii) 144

Here n is odd i.e, 3.

So, number of digits in square root = \(\frac { 3+1 }{ 2 } = 2\)

(iii) 4489

Here n is even i.e, 4.

Number of digits in square root =\( \frac { 4 }{ 2 } = 2\)

(iv) 27225

Here n is odd i.e, 5.

Number of digits in square root =\( \frac { 5+1 }{ 2 } = 3\)

(iv) 390625

Here n is even i.e, 6.

So, number of digits in square root =\( \frac { 6 }{ 2 } = 3\)