Question

What is the square root of $0.000441$ ?
(A) $0.021$
(B) $0.0021$
(C) $0.21$
(D) $2.1$

Answer 1

Hint: The question asks to find the square root of a given number, which is $0.000441$. We need to write that as $\sqrt {0.000441} $. Since it is expressed in decimals, we will convert it into a fraction such that the numerator and the denominator are perfect squares. Then, we can easily find the root of those numbers.

Complete step-by-step answer:
Let us consider the given number, $0.000441$
Let us convert it into fraction.
After the decimal, there are 6 digits. Therefore, we remove the decimal and the zeroes, and only keep the natural number. It is done as follows,
$0.000441 = \dfrac{{441}}{{10000000}}$
This can also be written as,
$0.000441 = \dfrac{{441}}{{{{10}^6}}}$
Now that we have the fraction, we write it under square root,
$\sqrt {\dfrac{{441}}{{{{10}^6}}}} $
The numerator is $441$ whose square root is $21$.
The exponent halved, gives us the square root of the denominator.
That is,
$ \Rightarrow \sqrt {\dfrac{{441}}{{{{10}^6}}}} = \dfrac{{21}}{{{{10}^3}}}$
Now, we need to convert the above fraction into decimal form again since the options are in decimals.
We make changes in the denominator,
$ \Rightarrow \dfrac{{21}}{{{{10}^3}}} = \dfrac{{21}}{{1000}}$
Since there are three zeroes in the denominator, the number in decimal will have three digits.
But the numerator is only two digits, so we place one more zero to the left, that is
$ \Rightarrow \dfrac{{21}}{{1000}} = 0.021$
Therefore, the final answer is $0.021$.
Hence, option (A) is the correct answer.
So, the correct answer is “Option A”.

Note: An alternate method in which the problem can be solved is keeping the decimal as it is under the root. Since there are three zeroes, we replace it by one and find the square root of only . Which will give the same answer.