Question

Find the number of digits in the square roots of each of the following numbers:
a. 64
b. 144
c. 4489
d. 27225
e. 390625

Answer 1

Hint: Count the number of digits and for even \[\left( \dfrac{n}{2} \right)\]and for odd \[\left( \dfrac{n+1}{2} \right)\]and we will get the number of digits in the square root of the numbers.

Complete step-by-step answer:
(a) 64
The number of digits in 64 = n = 2.
Here, n=2 is even
\[\therefore \]Number of digits in square root = \[\dfrac{n}{2}=\dfrac{2}{2}=1\]

(b) 144
Number of digits in 144 = n = 3
Here, n = 3 is odd
\[\therefore \]Number of digits in square root = \[\dfrac{n+1}{2}=\dfrac{3+1}{2}=2\]

(c) 4489
Number of digits in 4489 = n = 4
Here, n=4 is even
\[\therefore \]Number of digits in square root =\[\dfrac{n}{2}=\dfrac{4}{2}=2\]

(d) 27225
Number of digits in 27225 = n = 5
Here, n = 5 is odd
\[\therefore \]Number of digits in square root =\[\dfrac{n+1}{2}=\dfrac{5+1}{2}=\dfrac{6}{2}=3\]

(e) 390625
Number of digits in 390625 = n = 6
Here, n=6 is even
\[\therefore \]Number of digits in square root =\[\dfrac{n}{2}=\dfrac{6}{2}=3\]

Note:
(i) \[\sqrt{64}=8\], number of digits in square root = 1.
(ii) \[\sqrt{114}=12\], number of digits in square root = 2.
(iii) \[\sqrt{4489}=67\], number of digits in square root = 2.
(iv) \[\sqrt{27225}=165\], number of digits in square root = 3.
(v) \[\sqrt{390625}=625\], number of digits in square root = 3.