Question

Without calculating square roots, find the number of digits in the square root of the
following numbers.
i) 25600
(ii) 100000000
(iii) 36864
please help me in solving this. ​

Answer 1

$\huge\mathfrak\green{☟ \: \: \: answer \: \: \: \: \: ✎}$

$(i) \: 25600$

$:x = 5( \: an \: odd \: number)$

$: \: its \: square \: root \: will \: have \\ \: \frac{x + 1}{2} \: digits$

$i.e.. \: \frac{5 + 1}{2} = \frac{6}{2} = 3 \: digits$

$(ii) \: 100000000$

$: \: x = 9→ \: odd \: number$

: Number of digits of its square root

$= \frac{x + 1}{2} = \frac{9 + 1}{2} = \frac{10}{2} = 5$

$(iii) \: 36864$

$: \: x = 5→ \: odd \: number$

: Number of digits in its square root

$= \frac{x + 1}{2} = \frac{5 + 1}{2} = \frac{6}{2} = 3$

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