Calculate the square root of 26

Problem

√(,26)

Solution

1. Identify the number as a non-perfect square, since 5=25 and 6=36

2. Estimate the value by noting that 26 is very close to 25, meaning the result will be slightly larger than 5.

3. Apply the linear approximation formula ƒ*(x+Δ(x))≈ƒ(x)+ƒ(x)′*Δ(x) where ƒ(x)=√(,x) x=25 and Δ(x)=1

4. Calculate the derivative value at the perfect square: ƒ(25)′=1/(2√(,25))=1/10=0.1

5. Approximate the result: 5 + 0.1 = 5.1$.

6. Refine the value using a calculator for higher precision.

Final Answer

√(,26)≈5.09901951359

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