How do you simplify the square root of 13 144?

Answer 1

You can simplify the term by approximation! Here is the approach:

Let y = √x = x^(½). Then,

dy/dx = ½ * x^(-½) = 1/(2√x)

Select 115² to be x. Then, we obtain:

y = 115

dy/dx = 1/(2 * 115) = 1 / 230

Therefore, we obtain this equation:

y - 115 = 1/230 * (x - 115²)

If x = 13144, then we have:

y - 115 = 1/230 * (13144 - 115²)

y = 1/230 * (13144 - 115²) + 115

≈ 114.65

OR

What you can do is to factor out each term by term and extract the perfect square factor out of the √. For instance:

√(13144) = √(4 * 3286) = 2√3286