What is the fraction which when multiplied by itself gives 0.00053361?

Given: 

Given number is 0.00053361.

To do: 

We have to find the fraction that when multiplied by itself gives 0.00053361.

Solution:

Let the required fraction be $x$.

This implies,

$x^{2}=0.00053361$

$x=\sqrt{0.00053361}$

$=\sqrt{\frac{53361}{100000000}}$

$x=\frac{\sqrt{53361}}{\sqrt{100000000}}$

Therefore, the square root of 53361 is,

	231
2	53361 4
43	133 129
461	461     461
	0

$x=\frac{\sqrt{53361}}{\sqrt{100000000}}=\frac{231}{10000}$ 

Hence, the fraction which when multiplied by itself gives 227.798649 is $\frac{231}{10000}$ .