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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


Answer :

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 =\( \frac { 6 }{ 2 } = 3\)

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