How do I linearize a square root graph?

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To linearize a square root graph, one effective method is to plot y squared against x, as this will yield a linear relationship if y is proportional to the square root of x. Alternatively, using logarithmic scales for both variables can also help achieve a straight line. The original equation can be derived from the linearized data. This approach allows for easier analysis and understanding of the relationship between the variables. Understanding these transformations is crucial for accurately interpreting square root graphs.
Varad
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Homework Statement


These are the Points.
X values: 0, 1.98, 3.96, 5.94, 7.92, 9.9
Y values: 1.98, 7.13, 9.08, 11.04, 12.57, 14.51
I need to find the original equation and the linear equation. I can't seem to find the line for square root graphs.

2. The attempt at a solution

I know it's a square root graph, but that's about it.
 
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You know or suspect that ##y\propto\sqrt{x}##?
Then plot ##y^2## vs ##x##.
 
Simon Bridge said:
You know or suspect that ##y\propto\sqrt{x}##?
Then plot ##y^2## vs ##x##.
Thanks
 
Another way of getting a straight line is to plot the data using log scales for both variables.

Chet
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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