# Using Differentials to Approximate the Square Root of 49.5

In this tutorial we shall develop the differentials to approximate the value of $\sqrt {49.5}$.

The nearest number to 49.5 whose square root can be taken is 49, so let us consider that $x = 49$ and $\delta x = dx = 0.5$.

Now consider

Differentiating equation (i) with respect to $x$, we have

Taking the differential of equation (ii), we get

Using the values $x = 49$ and $dx = 0.5$, we have

Now