Find the decimal fraction which when multiplied by itself \[84.64\] ?

Hint:In this question, we need to find the decimal fraction which when multiplied by itself \[84.64\] . First, let us consider the decimal fraction as \[x\] . Here we can use the property \[x \times x = x^{2}\] . Then we need to convert the decimal number in terms of fraction because here we need to get rid of the decimal in the calculation part and also for easier conversion. On further simplifying, we can find the value of the \[x\] easily.

Complete step by step answer:
Here we need to find the decimal fraction which when multiplied by itself \[84.64\]. Let us consider the decimal fraction as \[x\]. Given that when multiplied by itself gives \[84.64\].
So \[x \times x = 84.64\]
We know that, \[x \times x = x^{2}\]
\[\Rightarrow \ x^{2} = 84.64\]
Now we can convert the given decimal number in fraction form.
Thus on multiplying both the numerator and denominator by \[100\]
We get,
\[\Rightarrow \ x^{2} = \dfrac{8464}{100}\]

Now on taking square root on both sides,
We get,
\[x = \sqrt{\dfrac{8464}{100}}\]
Now on taking the numbers out of radical sign,
We get,
\[x = \dfrac{92}{10}\]
On simplifying,
We get,
\[x = \dfrac{46}{5}\]
On further simplifying we get,
\[\therefore \ x = 9.2\]
Thus we get the number as \[9.2\].

Hence, \[9.2\] is the decimal fraction which when multiplied by itself gives \[84.64\].

Note:We can also use a calculator to simplify the final step. If we are using the calculator to find out the answer , we can simply enter the square root of \[84.64\] which will give us the correct answer. We should be very careful while taking the numbers out of the radical sign. We can also check whether our answer is correct or not by multiplying the decimal number \[9.2\] by itself, if it results \[84.64\] then our answer is absolutely correct.