Answer:
One way to estimate the cube root of 17576 is to use the fact that 20^3 = 8000 and 30^3 = 27000. Since 17576 is between 8000 and 27000, we know that its cube root is between 20 and 30.
To refine our estimate, we can use linear interpolation. Linear interpolation involves finding the equation of the line that passes through two known points and using that equation to estimate the value at a third point.
In this case, we know that:
20^3 = 8000
30^3 = 27000
The slope of the line passing through these two points is:
slope = (27000 - 8000) / (30 - 20) = 1900
The equation of the line passing through these two points is:
y - 8000 = 1900(x - 20)
where x is the value we want to estimate and y is the cube of x. Solving for y, we get:
y = 1900x - 23000
Substituting y = 17576, we get:
17576 = 1900x - 23000
Solving for x, we get:
x = (17576 + 23000) / 1900 = 21.8
Therefore, the cube root of 17576 is approximately 21.8.