Use linear interpolation between consecutive perfect squares to find find an approximation of each value. Round your answer to the nearest tenth. Using these rules how would I do this with 3?

I'm having some trouble figuring out how to do this, any chance someone could give an explanation how to solve it?

Thanks

1 Answer
Dec 25, 2017

See below. The answer is 31.7.

Explanation:

[What is linear interpolation?]
Linear interpolation is a method of curve fitting with linear plynomials.
Suppose two points A(x0,y0) and B(x1,y1) are given. If x0xx1, the value y can be approximated by substituting x to the formula of the line AB, that is, yy0=y1y0x1x0(xx0).
https://en.wikipedia.org/wiki/Linear_interpolationhttps://en.wikipedia.org/wiki/Linear_interpolation

[Solve this question]
In this question, 1=1 and 4=2 can be used for linear interpolation.

The formula of the line between A(1,1) and B(4,2) is as follows.
y1=2141(x1)
y1=13(x1)
y=13x+23

Substitute x=3 to the formula. The result is y=53=1.661.7

[This is your turn]
Then, how about trying to approximate 3 to the nearest hundredth using interpolation between C(2.89,1.7) and D(3.24,1.8)?
The answer will be 3303175=1.7311.73.