Question

What is the real square root of 0.0016?

Answer 1

Hint: We need to find the real root of 0.0016. So, we need to find $\sqrt{0.0016}$. For this we first need to convert the function under the square root in the square. So that we are able to cut the fractions and the whole number in powers and we get the answer. For this we will first convert the part under square root into fraction and then convert that as the square of some value.

Complete step-by-step answer:
We have 0.0016. We convert this into fraction, which is as follows:
$0.0016=\dfrac{16}{1000}$
Now, we know that $16=4\times 4$ and $1000=100\times 100$, so we can write it as follows:
$16=4^2$ and $10000=100^2$
So, the fraction can be written as:
$0.0016=\dfrac{4^2}{100^2}$
$\implies 0.0016=\left(\dfrac{4}{100}\right)^2$
So, till now we have obtained the following:
$0.0016=\dfrac{1}{25}^2$
Taking this under square root we get:
$\sqrt{0.0016}=\sqrt{\dfrac{1}{25^2}}$
Now, we use the following formula:
$\sqrt{a^2}=\pm a$
$\implies \sqrt{0.0016}=\sqrt{\dfrac{1}{25^2}}=\pm \dfrac{1}{25}$
Hence, the real square root of 0.0016 is $\dfrac{1}{25}$. Or we can write that the real square root of 0.0016 is 0.04.

Note: If you are sure about calculations you can simply do the square root of 16 which is 4 and later on adjust the zeros which may cause calculation mistakes. Adjusting the zeros can also be done using the powers of 10. For example, 0.0016 can be written as $16\times 10^{-4}$. After reducing this to half, we can write $4\times 10^{-2}$ which is again 0.04. This method is easier but is prone to calculation mistakes so do this only if you are sure that you won’t make any calculation mistake that may occur.