If y varies directly as the square root of x and y = 8 when x = 81, find y if x = 6561. (Round...

Question:

If y varies directly as the square root of x and y = 8 when x = 81, find y if x = 6561. (Round off your answer to the nearest hundredth.)

Directly Proportional

When two variables increase and decrease in value together, they are said to vary directly with each other or be directly proportional to each other. They can be related to each other by an equation by using a constant of proportionality.

As y varies directly as the square root of x, we have:

$$y=k\sqrt{x}$$

The value of the constant k can be found as follows using the fact that y = 8 when x = 81.

\begin{align} \Rightarrow 8&=k\sqrt{81}\\ \therefore k&=\frac 89 \end{align}

Now, when x=6561, the value of y will be:

\begin{align} y&=\frac{8}{9}*\sqrt{6561}\\ &=72 \end{align}