Question

Question 112

Solve the following question:

Find the decimal fraction, which when multiplied by itself, gives 84.64.

Answer 1

Let the decimal fraction be $x$.
When a decimal fractions is multiplied by itself, then product $=x\times x=x^2$ [given]
But product = 84.64
$\therefore x^2=84.64$
$\Rightarrow x=\sqrt{84.64}$
Now, place the bar over the numbers, then square root is given below.
$\begin{array}{cc}& 9.2\\ 9& \overline{84}.\overline{64}\\ & 81\\ 182& 364\\ & 364\\ & 0\end{array}$
$\therefore x=\sqrt{84.64}=9.2$
Hence, the required decimal is 9.2.