Approximating Square Roots Using Local Linearization

The video tutorial explains how to approximate the square root of 4.36 without a calculator by using the concept of local linearization. It begins by discussing the known value of the square root of 4 and introduces the function f(x) = sqrt(x). The tutorial then graphically represents the function and explains how to use the tangent line at x = 4 to approximate f(4.36). The derivative of the function is calculated to find the slope of the tangent line, which is then used to determine the approximate value of the square root. Finally, the approximation is validated using a calculator, showing that the method provides a close estimate.

What is the square root of 4?

• 3

• 1

• 2

• 4

What function is used to approximate the square root of 4.36?

• f(x) = 1/x

• f(x) = x^3

• f(x) = sqrt(x)

• f(x) = x^2

What is the purpose of using a tangent line in this approximation?

• To simplify the function

• To find the exact value

• To approximate values near a known point

• To calculate the derivative

What is the derivative of f(x) = sqrt(x) at x = 4?

• 1/4

• 2

• 1/2

• 1

What is the approximate value of the square root of 4.36 using local linearization?

• 2.00

• 2.20

• 2.09

• 2.10